Current Search:  Distribution Probability theory (x)

View All Items

  • CSV Spreadsheet
(1 - 3 of 3)
Determination of probability density from statistical moments by neural network approach
Title
Determination of probability density from statistical moments by neural network approach.
Creator
Zheng, Zhiyin., Florida Atlantic University, Cai, Guo-Qiang, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description
It is known that response probability densities, although important in failure analysis, are seldom achievable for stochastically excited systems except for linear systems under additive excitations of Gaussian processes. Most often, statistical moments are obtainable analytically or experimentally. It is proposed in this thesis to determine the probability density from the known statistical moments using artificial neural networks. A multi-layered feed-forward type of neural networks with...
Show moreIt is known that response probability densities, although important in failure analysis, are seldom achievable for stochastically excited systems except for linear systems under additive excitations of Gaussian processes. Most often, statistical moments are obtainable analytically or experimentally. It is proposed in this thesis to determine the probability density from the known statistical moments using artificial neural networks. A multi-layered feed-forward type of neural networks with error back-propagation training algorithm is proposed for the purpose and the parametric method is adopted for identifying the probability density function. Three examples are given to illustrate the applicability of the approach. All three examples show that the neural network approach gives quite accurate results in comparison with either the exact or simulation ones.
Show less
Date Issued
1996
PURL
http://purl.flvc.org/fcla/dt/15330
Subject Headings
Distribution (Probability theory), Moments method (Statistics), Estimation theory, Structural failures--Investigation, Neural networks (Computer science)
Format
Document (PDF)
Stochastic optimal impulse control of jump diffusions with application to exchange rate
Title
Stochastic optimal impulse control of jump diffusions with application to exchange rate.
Creator
Perera, Sandun C., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description
We generalize the theory of stochastic impulse control of jump diffusions introduced by Oksendal and Sulem (2004) with milder assumptions. In particular, we assume that the original process is affected by the interventions. We also generalize the optimal central bank intervention problem including market reaction introduced by Moreno (2007), allowing the exchange rate dynamic to follow a jump diffusion process. We furthermore generalize the approximation theory of stochastic impulse control...
Show moreWe generalize the theory of stochastic impulse control of jump diffusions introduced by Oksendal and Sulem (2004) with milder assumptions. In particular, we assume that the original process is affected by the interventions. We also generalize the optimal central bank intervention problem including market reaction introduced by Moreno (2007), allowing the exchange rate dynamic to follow a jump diffusion process. We furthermore generalize the approximation theory of stochastic impulse control problems by a sequence of iterated optimal stopping problems which is also introduced in Oksendal and Sulem (2004). We develop new results which allow us to reduce a given impulse control problem to a sequence of iterated optimal stopping problems even though the original process is affected by interventions.
Show less
Date Issued
2009
PURL
http://purl.flvc.org/FAU/3174308
Subject Headings
Management, Mathematical models, Control theory, Stochastic differential equations, Distribution (Probability theory), Optimal stopping (Mathematical statistics), Economics, Mathematical
Format
Document (PDF)
Simplicial matter in discrete and quantum spacetimes
Title
Simplicial matter in discrete and quantum spacetimes.
Creator
McDonald, Jonathan Ryan., Charles E. Schmidt College of Science, Department of Physics
Abstract/Description
A discrete formalism for General Relativity was introduced in 1961 by Tulio Regge in the form of a piecewise-linear manifold as an approximation to (pseudo-)Riemannian manifolds. This formalism, known as Regge Calculus, has primarily been used to study vacuum spacetimes as both an approximation for classical General Relativity and as a framework for quantum gravity. However, there has been no consistent effort to include arbitrary non-gravitational sources into Regge Calculus or examine the...
Show moreA discrete formalism for General Relativity was introduced in 1961 by Tulio Regge in the form of a piecewise-linear manifold as an approximation to (pseudo-)Riemannian manifolds. This formalism, known as Regge Calculus, has primarily been used to study vacuum spacetimes as both an approximation for classical General Relativity and as a framework for quantum gravity. However, there has been no consistent effort to include arbitrary non-gravitational sources into Regge Calculus or examine the structural details of how this is done. This manuscript explores the underlying framework of Regge Calculus in an effort elucidate the structural properties of the lattice geometry most useful for incorporating particles and fields. Correspondingly, we first derive the contracted Bianchi identity as a guide towards understanding how particles and fields can be coupled to the lattice so as to automatically ensure conservation of source. In doing so, we derive a Kirchhoff-like conservation principle that identifies the flow of energy and momentum as a flux through the circumcentric dual boundaries. This circuit construction arises naturally from the topological structure suggested by the contracted Bianchi identity. Using the results of the contracted Bianchi identity we explore the generic properties of the local topology in Regge Calculus for arbitrary triangulations and suggest a first-principles definition that is consistent with the inclusion of source. This prescription for extending vacuum Regge Calculus is sufficiently general to be applicable to other approaches to discrete quantum gravity. We discuss how these findings bear on a quantized theory of gravity in which the coupling to source provides a physical interpretation for the approximate invariance principles of the discrete theory.
Show less
Date Issued
2009
PURL
http://purl.flvc.org/FAU/186691
Subject Headings
Special relativity (Physics), Space and time, Distribution (Probability theory), Global differential geometry, Quantum field theory, Mathematical physics
Format
Document (PDF)