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Numerical path integration of stochastic systems
Title
Numerical path integration of stochastic systems.
Creator
Yu, Jinshou., Florida Atlantic University, Lin, Y. K., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description
The present dissertation is focused on the numerical method of path integration for stochastic systems. The existing procedures of numerical path integration are re-examined. A comparison study is made of the results obtained using various interpolation schemes. The amounts of computation time and relative accuracies of the existing procedures are tested with different mesh sizes and different time step sizes. A new numerical procedure based on Gauss-Legendre integration formula is proposed,...
Show moreThe present dissertation is focused on the numerical method of path integration for stochastic systems. The existing procedures of numerical path integration are re-examined. A comparison study is made of the results obtained using various interpolation schemes. The amounts of computation time and relative accuracies of the existing procedures are tested with different mesh sizes and different time step sizes. A new numerical procedure based on Gauss-Legendre integration formula is proposed, which requires no explicit numerical interpolation. The probability evolution is represented in terms of the transition probabilities among Gauss points in various sub-intervals. Each transition probability is assumed to be Gaussian, and it can be obtained from the moment equations. Gaussian closure is used to truncate the moment equations in the case of a nonlinear system. The computation parameters of the new procedure, such as size of time-step and number of sub-intervals, can be determined in a systematic manner. The approximate Gaussianity of the transition probability obtained from the moment equations is first tested by comparing it with the simulation results, from which a proper time-step size is selected. The standard deviation of the transition probability in each direction of the state space can then be obtained from the moment equations, and is used to determine the size of the sub-intervals in that direction. The new numerical path integration procedure is applied to several one-dimensional and two-dimensional stochastic systems, for which the responses are homogeneous Markov processes. It is shown that the new procedure is not only accurate and efficient, but also numerically stable and highly adaptable. The new procedure is also applied to a nonlinear stochastic system subjected to both sinusoidal and random excitations. The system response in this case is a non-homogeneous Markov process. The algorithm is adapted for this case, so that re-computation of the transition probability density at every time step can be avoided.
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Date Issued
1997
PURL
http://purl.flvc.org/fcla/dt/12506
Subject Headings
Stochastic systems, Numerical integration, Markov processes
Format
Document (PDF)
Application of MoM: Scattering calculations using condition number
Title
Application of MoM: Scattering calculations using condition number.
Creator
Zhuang, Zhijun., Florida Atlantic University, Bagby, Jonathan S., College of Engineering and Computer Science, Department of Computer and Electrical Engineering and Computer Science
Abstract/Description
Computational accuracy is widely recognized as a critical issue in applied electromagnetics. Increasing computational power is being applied to solve more complex electromagnetic systems with an emphasis on computational accuracy. The work of this thesis is focused on the implementation of Method of Moments (MoM) to integral equation formulations. The goal of this effort is to use what is known as condition number, and, a heuristic rule-of-thumb is applied to investigate the computational...
Show moreComputational accuracy is widely recognized as a critical issue in applied electromagnetics. Increasing computational power is being applied to solve more complex electromagnetic systems with an emphasis on computational accuracy. The work of this thesis is focused on the implementation of Method of Moments (MoM) to integral equation formulations. The goal of this effort is to use what is known as condition number, and, a heuristic rule-of-thumb is applied to investigate the computational accuracy of MoM in numerical electromagnetics. Other possible applications of condition number of the MoM matrix are also indicated.
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Date Issued
1999
PURL
http://purl.flvc.org/fcla/dt/15719
Subject Headings
Electromagnetism, Moments method (Statistics), Electromagnetic theory, Integral equations--Numerical solutions
Format
Document (PDF)
Performance analysis of linear diversity schemes in generalized gamma fading channels
Title
Performance analysis of linear diversity schemes in generalized gamma fading channels.
Creator
Piboongungon, Terawat., Florida Atlantic University, Aalo, Valentine A., College of Engineering and Computer Science, Department of Computer and Electrical Engineering and Computer Science
Abstract/Description
The main focus of this dissertation is to analyze the performance of linear diversity schemes operating in generalized gamma fading channels. The generalized gamma fading model is a versatile fading envelope that generalizes many of commonly used statistical models that describe signal fluctuations due to multipath, shadowing, or a mixture of such processes. The traditional linear diversity combining techniques such as maximal ratio combining (MRC), equal gain combining (EGC), and selection...
Show moreThe main focus of this dissertation is to analyze the performance of linear diversity schemes operating in generalized gamma fading channels. The generalized gamma fading model is a versatile fading envelope that generalizes many of commonly used statistical models that describe signal fluctuations due to multipath, shadowing, or a mixture of such processes. The traditional linear diversity combining techniques such as maximal ratio combining (MRC), equal gain combining (EGC), and selection combining (SC) are addressed with reference to generalized gamma fading environments. For the special case of Nakagami fading, new expressions for outage probability and error-rate performance of linear diversity schemes with arbitrary fading parameters are derived in terms of the Lauricella function. Effects of correlated fading are also studied. Their fruitful application to third generation (3G) wideband code division multiple access (WCDMA) systems, particularly for multiple-input multiple-output (MIMO) and 2D-RAKE receivers are demonstrated. The results exhibit a finite integral representation that can be used for fast and accurate numerical computation. A detail study is also done on multivariate generalized gamma fading environments. Relevant statistical characterization of the sum of independent generalized gamma random variables is derived and expressed in terms of the multivariable Fox's H-function. Since numerical evaluation for the multivariate Fox's H-function is difficult, simpler numerical computations are developed using moment generating function and characteristic function approaches. Since some wireless applications may not have enough space among diversity branches, the statistical characterizations of multivariate correlated generalized gamma fading are relevant in such cases. An investigation on the outage performance for multi-branch selection combining is performed for the correlated multivariate generalized gamma channel. Finally, the dissertation summarizes the main results and explores some directions for further studies.
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Date Issued
2005
PURL
http://purl.flvc.org/fcla/dt/12135
Subject Headings
Numerical integration, Wireless communication systems--Mathematical models, Frequency spectra--Mathematical models
Format
Document (PDF)