Current Search: info:fedora/islandora:entityCModel (x) » FAU (x) » Department of Mathematical Sciences (x)
View All Items
Pages
 Title
 Bayesian approach to an exponential hazard regression model with a change point.
 Creator
 Abraha, Yonas Kidane, Qian, Lianfen, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

This thesis contains two parts. The first part derives the Bayesian estimator of the parameters in a piecewise exponential Cox proportional hazard regression model, with one unknown change point for a right censored survival data. The second part surveys the applications of change point problems to various types of data, such as longterm survival data, longitudinal data and time series data. Furthermore, the proposed method is then used to analyse a real survival data.
 Date Issued
 2014
 PURL
 http://purl.flvc.org/fau/fd/FA00004013
 Subject Headings
 Bayesian statistical decision theory, Mathematical statistics, Multivariate analysis  Data processing
 Format
 Document (PDF)
 Title
 On the spectrum of positive operators.
 Creator
 Acharya, Cheban P., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

Spectral theory, mathematical system theory, evolution equations, differential and difference equations [electronic resource] : 21st International Workshop on Operator Theory and Applications, Berlin, July 2010.It is known that lattice homomorphisms and Gsolvable positive operators on Banach lattices have cyclic peripheral spectrum (See [17]). In my thesis I prove that positive contractions whose spectral radius is 1 on Banach lattices with increasing norm have cyclic peripheral point...
Show moreSpectral theory, mathematical system theory, evolution equations, differential and difference equations [electronic resource] : 21st International Workshop on Operator Theory and Applications, Berlin, July 2010.It is known that lattice homomorphisms and Gsolvable positive operators on Banach lattices have cyclic peripheral spectrum (See [17]). In my thesis I prove that positive contractions whose spectral radius is 1 on Banach lattices with increasing norm have cyclic peripheral point spectrum. I also prove that if the Banach lattice is a K B space satisfying the growth conditon and º is an eigenvalue of a positive contraction T such that [º] = 1, then 1 is also an eigenvalue of T as well as an eigenvalue of T¨, the dual of T. I also investigate the conditions on contraction operators on Hilbert lattices and ALspaces which guanantee that 1 is an eigenvalue. As we know from [17], if T : EE is a positive ideal irreducible operator on E such the r (T) = 1 is a pole of the resolvent R(º, T), then r (T) is simple pole with dimN (T r(T)I) and ºper(T) is cyclic. Also all points of ºper(T) are simple poles of the resolvent R(º,T). SInce band irreducibility and ºorder continuity do not imply ideal irreducibility [2], we prove the analogous results for band irreducible, ºorder continuous operators.
Show less  Date Issued
 2012
 PURL
 http://purl.flvc.org/FAU/3359288
 Subject Headings
 Operator theory, Evolution equations, Banach spaces, Linear topological spaces, Functional analysis
 Format
 Document (PDF)
 Title
 Curve shortening in secondorder lagrangian.
 Creator
 Adams, Ronald Edward, Kalies, William D., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

A secondorder Lagrangian system is a generalization of a classical mechanical system for which the Lagrangian action depends on the second derivative of the state variable. Recent work has shown that the dynamics of such systems c:an be substantially richer than for classical Lagrangian systems. In particular, topological properties of the planar curves obtained by projection onto the lowerorder derivatives play a key role in forcing certain types of dynamics. However, the application of...
Show moreA secondorder Lagrangian system is a generalization of a classical mechanical system for which the Lagrangian action depends on the second derivative of the state variable. Recent work has shown that the dynamics of such systems c:an be substantially richer than for classical Lagrangian systems. In particular, topological properties of the planar curves obtained by projection onto the lowerorder derivatives play a key role in forcing certain types of dynamics. However, the application of these techniques requires an analytic restriction on the Lagrangian that it satisfy a twist property. In this dissertation we approach this problem from the point of view of curve shortening in an effort to remove the twist condition. In classical curve shortening a family of curves evolves with a velocity which is normal to the curve and proportional to its curvature. The evolution of curves with decreasing action is more general, and in the first part of this dissertation we develop some results for curve shortening flows which shorten lengths with respect to a Finsler metric rather than a Riemannian metric. The second part of this dissertation focuses on analytic methods to accommodate the fact that the Finsler metric for secondorder Lagrangian system has singularities. We prove the existence of simple periodic solutions for a general class of systems without requiring the twist condition. Further; our results provide a frame work in which to try to further extend the topological forcing theorems to systems without the twist condition.
Show less  Date Issued
 2014
 PURL
 http://purl.flvc.org/fau/fd/FA00004175, http://purl.flvc.org/fau/fd/FA00004175
 Subject Headings
 Critical point theory (Mathematical analysis), Differentiable dynamical systems, Geometry,Differential, Lagrange equations, Lagrangian functions, Mathematical optimization, Surfaces of constant curvature
 Format
 Document (PDF)
 Title
 Computing automorphism groups of projective planes.
 Creator
 Adamski, Jesse Victor, Magliveras, Spyros S., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

The main objective of this thesis was to find the full automorphism groups of finite Desarguesian planes. A set of homologies were used to generate the automorphism group when the order of the plane was prime. When the order was a prime power Pa,a ≠ 1 the Frobenius automorphism was added to the set of homologies, and then the full automorphism group was generated. The Frobenius automorphism was found by using the planar ternary ring derived from a coordinatization of the plane.
 Date Issued
 2013
 PURL
 http://purl.flvc.org/fau/fd/FA0004000
 Subject Headings
 Combinatorial group theory, Finite geometrics, Geometry, Projective
 Format
 Document (PDF)
 Title
 Message authentication in an identitybased encryption scheme: 1KeyEncryptThenMAC.
 Creator
 Amento, Brittanney Jaclyn, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

We present an IdentityBased Encryption scheme, 1KeyEncryptThenMAC, in which we are able to verify the authenticity of messages using a MAC. We accomplish this authentication by combining an IdentityBased Encryption scheme given by Boneh and Franklin, with an IdentityBased NonInteractive Key Distribution given by Paterson and Srinivasan, and attaching a MAC. We prove the scheme is chosen plaintext secure and chosen ciphertext secure, and the MAC is existentially unforgeable.
 Date Issued
 2010
 PURL
 http://purl.flvc.org/FAU/2796050
 Subject Headings
 Data encryption (Computer science), Public key cryptopgraphy, Public key infrastructure (Computer security)
 Format
 Document (PDF)
 Title
 Quantum Circuits for Cryptanalysis.
 Creator
 Amento, Brittanney Jaclyn, Steinwandt, Rainer, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

Finite elds of the form F2m play an important role in coding theory and cryptography. We show that the choice of how to represent the elements of these elds can have a signi cant impact on the resource requirements for quantum arithmetic. In particular, we show how the Gaussian normal basis representations and \ghostbit basis" representations can be used to implement inverters with a quantum circuit of depth O(mlog(m)). To the best of our knowledge, this is the rst construction with...
Show moreFinite elds of the form F2m play an important role in coding theory and cryptography. We show that the choice of how to represent the elements of these elds can have a signi cant impact on the resource requirements for quantum arithmetic. In particular, we show how the Gaussian normal basis representations and \ghostbit basis" representations can be used to implement inverters with a quantum circuit of depth O(mlog(m)). To the best of our knowledge, this is the rst construction with subquadratic depth reported in the literature. Our quantum circuit for the computation of multiplicative inverses is based on the ItohTsujii algorithm which exploits the property that, in a normal basis representation, squaring corresponds to a permutation of the coe cients. We give resource estimates for the resulting quantum circuit for inversion over binary elds F2m based on an elementary gate set that is useful for faulttolerant implementation. Elliptic curves over nite elds F2m play a prominent role in modern cryptography. Published quantum algorithms dealing with such curves build on a short Weierstrass form in combination with a ne or projective coordinates. In this thesis we show that changing the curve representation allows a substantial reduction in the number of Tgates needed to implement the curve arithmetic. As a tool, we present a quantum circuit for computing multiplicative inverses in F2m in depth O(mlogm) using a polynomial basis representation, which may be of independent interest. Finally, we change our focus from the design of circuits which aim at attacking computational assumptions on asymmetric cryptographic algorithms to the design of a circuit attacking a symmetric cryptographic algorithm. We consider a block cipher, SERPENT, and our design of a quantum circuit implementing this cipher to be used for a key attack using Grover's algorithm as in [18]. This quantum circuit is essential for understanding the complexity of Grover's algorithm.
Show less  Date Issued
 2016
 PURL
 http://purl.flvc.org/fau/fd/FA00004662, http://purl.flvc.org/fau/fd/FA00004662
 Subject Headings
 Artificial intelligence, Computer networks, Cryptography, Data encryption (Computer science), Finite fields (Algebra), Quantum theory
 Format
 Document (PDF)
 Title
 ON SOLUTIONS OF A PERTURBED SCHROEDINGER EQUATION.
 Creator
 ARTERO, AGUSTIN., Florida Atlantic University, Schonbek, Tomas P., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

We study L^2 (R^k) solutions of the equation [..] where [..] and V is a nonnegative L^2 function. Our main results are Theorems 1 and 2 of Chapter IV, in which we prove that these solutions depend continuously on V.
 Date Issued
 1975
 PURL
 http://purl.flvc.org/fcla/dt/13716
 Subject Headings
 Schrödinger equation
 Format
 Document (PDF)
 Title
 Unique decomposition of direct sums of ideals.
 Creator
 Ay, Basak., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

We say that a commutative ring R has the unique decomposition into ideals (UDI) property if, for any Rmodule which decomposes into a finite direct sum of indecomposable ideals, this decomposition is unique up to the order and isomorphism class of the ideals. In a 2001 paper, Goeters and Olberding characterize the UDI property for Noetherian integral domains. In Chapters 13 the UDI property for reduced Noetherian rings is characterized. In Chapter 4 it is shown that overrings of one...
Show moreWe say that a commutative ring R has the unique decomposition into ideals (UDI) property if, for any Rmodule which decomposes into a finite direct sum of indecomposable ideals, this decomposition is unique up to the order and isomorphism class of the ideals. In a 2001 paper, Goeters and Olberding characterize the UDI property for Noetherian integral domains. In Chapters 13 the UDI property for reduced Noetherian rings is characterized. In Chapter 4 it is shown that overrings of onedimensional reduced commutative Noetherian rings with the UDI property have the UDI property, also. In Chapter 5 we show that the UDI property implies the KrullSchmidt property for direct sums of torsionfree rank one modules for a reduced local commutative Noetherian onedimensional ring R.
Show less  Date Issued
 2010
 PURL
 http://purl.flvc.org/FAU/2683133
 Subject Headings
 Algebraic number theory, Modules (Algebra), Noetherian rings, Commutative rings, Algebra, Abstract
 Format
 Document (PDF)
 Title
 CHARACTERIZATIONS OF LINEAR ISOMETRIES ON COMPLEX SEQUENCE SPACES.
 Creator
 Babun Codorniu, Omar, Zhang, XiaoDong, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
 Abstract/Description

An operator acting on a Banach space is called an isometry if it preserves the norm of the space. An interesting problem is to determine the form or structure of linear isometries on Banach spaces. This can be done in some instances. This dissertation presents several theorems that provide necessary and sufficient conditions for some linear operators acting on finite and infinite dimensional sequence spaces of complex numbers to be isometries. In all cases, the linear isometries have the form...
Show moreAn operator acting on a Banach space is called an isometry if it preserves the norm of the space. An interesting problem is to determine the form or structure of linear isometries on Banach spaces. This can be done in some instances. This dissertation presents several theorems that provide necessary and sufficient conditions for some linear operators acting on finite and infinite dimensional sequence spaces of complex numbers to be isometries. In all cases, the linear isometries have the form of a permutation of the elements of the sequences in the given space, with each component of each sequence multiplied by a complex number of absolute value 1.
Show less  Date Issued
 2019
 PURL
 http://purl.flvc.org/fau/fd/FA00013354
 Subject Headings
 Banach spaces, Isometrics (Mathematics), Matrices, Linear operators, Normed linear spaces
 Format
 Document (PDF)
 Title
 THE CHANGE POINT PROBLEM FOR TWO CLASSES OF STOCHASTIC PROCESSES.
 Creator
 Ball, Cory, Long, Hongwei, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
 Abstract/Description

The change point problem is a problem where a process changes regimes because a parameter changes at a point in time called the change point. The objective of this problem is to estimate the change point and each of the parameters of the stochastic process. In this thesis, we examine the change point problem for two classes of stochastic processes. First, we consider the volatility change point problem for stochastic diffusion processes driven by Brownian motions. Then, we consider the drift...
Show moreThe change point problem is a problem where a process changes regimes because a parameter changes at a point in time called the change point. The objective of this problem is to estimate the change point and each of the parameters of the stochastic process. In this thesis, we examine the change point problem for two classes of stochastic processes. First, we consider the volatility change point problem for stochastic diffusion processes driven by Brownian motions. Then, we consider the drift change point problem for OrnsteinUhlenbeck processes driven by _stable Levy motions. In each problem, we establish the consistency of the estimators, determine asymptotic behavior for the changing parameters, and finally, we perform simulation studies to computationally assess the convergence of parameters.
Show less  Date Issued
 2020
 PURL
 http://purl.flvc.org/fau/fd/FA00013462
 Subject Headings
 Stochastic processes, Changepoint problems, Brownian motion processes, OrnsteinUhlenbeck process, Computer simulation
 Format
 Document (PDF)
 Title
 Derivation of planar diffeomorphisms from Hamiltonians with a kick.
 Creator
 Barney, Zalmond C., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

In this thesis we will discuss connections between Hamiltonian systems with a periodic kick and planar diffeomorphisms. After a brief overview of Hamiltonian theory we will focus, as an example, on derivations of the Hâenon map that can be obtained by considering kicked Hamiltonian systems. We will conclude with examples of Hâenon maps of interest.
 Date Issued
 2011
 PURL
 http://purl.flvc.org/FAU/3329833
 Subject Headings
 Mathematical physics, Differential equations, Partial, Hamiltonian systems, Algebra, Linear, Chaotic behavior in systems
 Format
 Document (PDF)
 Title
 Norm Inequalities for the Fourier Coefficients of Some Almost Periodic Functions.
 Creator
 Boryshchak, Yarema, Sagher, Yoram, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

Using C. Fefferman's embedding of a charge space in a measure space allows us to apply standard interpolation theorems to the establishment of norm inequalities for Besicovitch almost periodic functions. This yields a significant improvement to the results of A. Avantaggiati, G. Bruno and R. Iannacci.
 Date Issued
 2019
 PURL
 http://purl.flvc.org/fau/fd/FA00013191
 Subject Headings
 Fourier series, Almost periodic functions, Norm
 Format
 Document (PDF)
 Title
 Algebraic and combinatorial aspects of group factorizations.
 Creator
 Bozovic, Vladimir., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

The aim of this work is to investigate some algebraic and combinatorial aspects of group factorizations. The main contribution of this dissertation is a set of new results regarding factorization of groups, with emphasis on the nonabelian case. We introduce a novel technique for factorization of groups, the socalled free mappings, a powerful tool for factorization of a wide class of abelian and nonabelian groups. By applying a certain group action on the blocks of a factorization, a number...
Show moreThe aim of this work is to investigate some algebraic and combinatorial aspects of group factorizations. The main contribution of this dissertation is a set of new results regarding factorization of groups, with emphasis on the nonabelian case. We introduce a novel technique for factorization of groups, the socalled free mappings, a powerful tool for factorization of a wide class of abelian and nonabelian groups. By applying a certain group action on the blocks of a factorization, a number of combinatorial and computational problems were noted and studied. In particular, we analyze the case of the group Aut(Zn) acting on blocks of factorization of Zn. We present new theoretical facts that reveal the numerical structure of the stabilizer of a set in Zn, under the action of Aut(Zn). New algorithms for finding the stabilizer of a set and checking whether two sets belong to the same orbit are proposed.
Show less  Date Issued
 2008
 PURL
 http://purl.flvc.org/FAU/107805
 Subject Headings
 Physical measurements, Mapping (Mathematics), Combinatorial enumeration problems, Algebra, Abstract
 Format
 Document (PDF)
 Title
 Asymmetric information in fads models in Lâevy markets.
 Creator
 Buckley, Winston S., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

Fads models for stocks under asymmetric information in a purely continuous(GBM) market were first studied by P. Guasoni (2006), where optimal portfolios and maximum expected logarithmic utilities, including asymptotic utilities for the informed and uninformed investors, were presented. We generalized this theory to Lâevy markets, where stock prices and the process modeling the fads are allowed to include a jump component, in addition to the usual continuous component. We employ the methods of...
Show moreFads models for stocks under asymmetric information in a purely continuous(GBM) market were first studied by P. Guasoni (2006), where optimal portfolios and maximum expected logarithmic utilities, including asymptotic utilities for the informed and uninformed investors, were presented. We generalized this theory to Lâevy markets, where stock prices and the process modeling the fads are allowed to include a jump component, in addition to the usual continuous component. We employ the methods of stochastic calculus and optimization to obtain analogous results to those obtained in the purely continuous market. We approximate optimal portfolios and utilities using the instantaneous centralized and quasicentralized moments of the stocks percentage returns. We also link the random portfolios of the investors, under asymmetric information to the purely deterministic optimal portfolio, under symmetric information.
Show less  Date Issued
 2009
 PURL
 http://purl.flvc.org/FAU/3337187
 Subject Headings
 Investments, Mathematical models, Capital market, Mathematical models, Finance, Mathematical models, Information theory in economics, Capital asset pricing model, Lâevy processes
 Format
 Document (PDF)
 Title
 Elliptic curves: identitybased signing and quantum arithmetic.
 Creator
 Budhathoki, Parshuram, Steinwandt, Rainer, Eisenbarth, Thomas, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

Pairingfriendly curves and elliptic curves with a trapdoor for the discrete logarithm problem are versatile tools in the design of cryptographic protocols. We show that curves having both properties enable a deterministic identitybased signing with “short” signatures in the random oracle model. At PKC 2003, Choon and Cheon proposed an identitybased signature scheme along with a provable security reduction. We propose a modification of their scheme with several performance benefits. In...
Show morePairingfriendly curves and elliptic curves with a trapdoor for the discrete logarithm problem are versatile tools in the design of cryptographic protocols. We show that curves having both properties enable a deterministic identitybased signing with “short” signatures in the random oracle model. At PKC 2003, Choon and Cheon proposed an identitybased signature scheme along with a provable security reduction. We propose a modification of their scheme with several performance benefits. In addition to faster signing, for batch signing the signature size can be reduced, and if multiple signatures for the same identity need to be verified, the verification can be accelerated. Neither the signing nor the verification algorithm rely on the availability of a (pseudo)random generator, and we give a provable security reduction in the random oracle model to the (`)Strong DiffieHellman problem. Implementing the group arithmetic is a costcritical task when designing quantum circuits for Shor’s algorithm to solve the discrete logarithm problem. We introduce a tool for the automatic generation of addition circuits for ordinary binary elliptic curves, a prominent platform group for digital signatures. Our Python software generates circuit descriptions that, without increasing the number of qubits or Tdepth, involve less than 39% of the number of Tgates in the best previous construction. The software also optimizes the (CNOT) depth for F2linear operations by means of suitable graph colorings.
Show less  Date Issued
 2014
 PURL
 http://purl.flvc.org/fau/fd/FA00004182, http://purl.flvc.org/fau/fd/FA00004182
 Subject Headings
 Coding theory, Computer network protocols, Computer networks  Security measures, Data encryption (Computer science), Mathematical physics, Number theory  Data processing
 Format
 Document (PDF)
 Title
 A study of divisors and algebras on a double cover of the affine plane.
 Creator
 Bulj, Djordje., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

An algebraic surface defined by an equation of the form z2 = (x+a1y) ... (x + any) (x  1) is studied, from both an algebraic and geometric point of view. It is shown that the surface is rational and contains a singular point which is nonrational. The class group of Weil divisors is computed and the Brauer group of Azumaya algebras is studied. Viewing the surface as a cyclic cover of the affine plane, all of the terms in the cohomology sequence of Chase, Harrison and Roseberg are computed.
 Date Issued
 2012
 PURL
 http://purl.flvc.org/FAU/3355618
 Subject Headings
 Algebraic number theory, Geometry, Data processing, Noncommutative differential geometry, Mathematical physics, Curves, Algebraic, Commutative rings
 Format
 Document (PDF)
 Title
 On projected planes.
 Creator
 Caliskan, Cafer., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

This work was motivated by the wellknown question: "Does there exist a nondesarguesian projective plane of prime order?" For a prime p 1, determine all subplanes of order p up to collineations, and check whether one of these is nondesarguesian." In this manuscript we use a grouptheoretic methodology to determine the subplane structures of some nondesarguesian planes. In particular, we determine orbit representatives of all proper Qsubplanes both of a VeblenWedderburn (VW) plane of...
Show moreThis work was motivated by the wellknown question: "Does there exist a nondesarguesian projective plane of prime order?" For a prime p < 11, there is only the pappian plane of order p. Hence, such planes are indeed desarguesian. Thus, it is of interest to examine whether there are nondesarguesian planes of order 11. A suggestion by Ascher Wagner in 1985 was made to Spyros S. Magliveras: "Begin with a nondesarguesian plane of order pk, k > 1, determine all subplanes of order p up to collineations, and check whether one of these is nondesarguesian." In this manuscript we use a grouptheoretic methodology to determine the subplane structures of some nondesarguesian planes. In particular, we determine orbit representatives of all proper Qsubplanes both of a VeblenWedderburn (VW) plane of order 121 and of the Hughes plane of order 121, under their full collineation groups. In PI, there are 13 orbits of Baer subplanes, all of which are desarguesian, and approximately 3000 orbits of Fano subplanes. In Sigma , there are 8 orbits of Baer subplanes, all of which are desarguesian, 2 orbits of subplanes of order 3, and at most 408; 075 distinct Fano subplanes. In addition to the above results, we also study the subplane structures of some nondesarguesian planes, such as the Hall plane of order 25, the Hughes planes of order 25 and 49, and the Figueora planes of order 27 and 125. A surprising discovery by L. Puccio and M. J. de Resmini was the existence of a plane of order 3 in the Hughes plane of order 25. We generalize this result, showing that there are subplanes of order 3 in the Hughes planes of order q2, where q is a prime power and q 5 (mod 6). Furthermore, we analyze the structure of the full collineation groups of certain Veblen Wedderburn (VW) planes of orders 25, 49 and 121, and discuss how to recover the planes from their collineation groups.
Show less  Date Issued
 2010
 PURL
 http://purl.flvc.org/FAU/1927609
 Subject Headings
 Projected planes, Combinatorial designs and configurations, Surfaces, Algebraic, Manifolds (Mathematics)
 Format
 Document (PDF)
 Title
 AUC estimation under various survival models.
 Creator
 Chang, Fazhe., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

In the medical science, the receiving operationg characteristic (ROC) curve is a graphical representation to evaluate the accuracy of a medical diagnostic test for any cutoff point. The area under the ROC curve (AUC) is an overall performance measure for a diagnostic test. There are two parts in this dissertation. In the first part, we study the properties of biExponentiated Weibull models. FIrst, we derive a general moment formula for single Exponentiated Weibull models. Then we move on to...
Show moreIn the medical science, the receiving operationg characteristic (ROC) curve is a graphical representation to evaluate the accuracy of a medical diagnostic test for any cutoff point. The area under the ROC curve (AUC) is an overall performance measure for a diagnostic test. There are two parts in this dissertation. In the first part, we study the properties of biExponentiated Weibull models. FIrst, we derive a general moment formula for single Exponentiated Weibull models. Then we move on to derive the precise formula of AUC and study the maximus likelihood estimation (MLE) of the AUC. Finally, we obtain the asymptotoc distribution of the estimated AUC. Simulation studies are used to check the performance of MLE of AUC under the moderate sample sizes. The second part fo the dissertation is to study the estimation of AUC under the crossing model, which extends the AUC formula in Gonen and Heller (2007).
Show less  Date Issued
 2012
 PURL
 http://purl.flvc.org/FAU/3359287
 Subject Headings
 Receiver operating characteristic curves, Medical screening, Statistical methods, Diagnosis, Statistical methods, Smoothing (Statistics)
 Format
 Document (PDF)
 Title
 PARAMETER ESTIMATION FOR GEOMETRIC L EVY PROCESSES WITH STOCHASTIC VOLATILITY.
 Creator
 Chhetri, Sher B., Long, Hongwei, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

In finance, various stochastic models have been used to describe the price movements of financial instruments. After Merton's [38] seminal work, several jump diffusion models for option pricing and risk management have been proposed. In this dissertation, we add alphastable Levy motion to the process related to dynamics of logreturns in the BlackScholes model where the volatility is assumed to be constant. We use the sample characteristic function approach in order to study parameter...
Show moreIn finance, various stochastic models have been used to describe the price movements of financial instruments. After Merton's [38] seminal work, several jump diffusion models for option pricing and risk management have been proposed. In this dissertation, we add alphastable Levy motion to the process related to dynamics of logreturns in the BlackScholes model where the volatility is assumed to be constant. We use the sample characteristic function approach in order to study parameter estimation for discretely observed stochastic differential equations driven by Levy noises. We also discuss the consistency and asymptotic properties of the proposed estimators. Simulation results of the model are also presented to show the validity of the estimators. We then propose a new model where the volatility is not a constant. We consider generalized alphastable geometric Levy processes where the stochastic volatility follows the CoxIngersollRoss (CIR) model in Cox et al. [9]. A number of methods have been proposed for estimating parameters for stable laws. However, a complication arises in estimation of the parameters in our model because of the presence of the unobservable stochastic volatility. To combat this complication we use the sample characteristic function method proposed by Press [48] and the conditional least squares method as mentioned in Overbeck and Ryden [47] to estimate all the parameters. We then discuss the consistency and asymptotic properties of the proposed estimators and establish a Central Limit Theorem. We perform simulations to assess the validity of the estimators. We also present several tables to show the comparison of estimators using different choices of arguments ui's. We conclude that all the estimators converge as expected regardless of the choice of ui's.
Show less  Date Issued
 2019
 PURL
 http://purl.flvc.org/fau/fd/FA00013294
 Subject Headings
 Stochastic models, Lévy processes, Parameter estimation, Finance, Simulations
 Format
 Document (PDF)
 Title
 Minimal zerodimensional extensions.
 Creator
 Chiorescu, Marcela, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

The structure of minimal zerodimensional extension of rings with Noetherian spectrum in which zero is a primary ideal and with at most one prime ideal of height greater than one is determined. These rings include K[[X,T]] where K is a field and Dedenkind domains, but need not be Noetherian nor integrally closed. We show that for such a ring R there is a onetoone correspondence between isomorphism classes of minimal zerodimensional extensions of R and sets M, where the elements of M are...
Show moreThe structure of minimal zerodimensional extension of rings with Noetherian spectrum in which zero is a primary ideal and with at most one prime ideal of height greater than one is determined. These rings include K[[X,T]] where K is a field and Dedenkind domains, but need not be Noetherian nor integrally closed. We show that for such a ring R there is a onetoone correspondence between isomorphism classes of minimal zerodimensional extensions of R and sets M, where the elements of M are ideals of R primary for distinct prime ideals of height greater than zero. A subsidiary result is the classification of minimal zerodimensional extensions of general ZPIrings.
Show less  Date Issued
 2009
 PURL
 http://purl.flvc.org/FAU/210447
 Subject Headings
 Algebra, Abstract, Noetherian rings, Commutative rings, Modules (Algebra), Algebraic number theory
 Format
 Document (PDF)