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Stochastic Approximations Via Large Deviations Asymptotic Properties
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Book Synopsis Stochastic Approximations Via Large Deviations: Asymptotic Properties by : Paul Dupuis
Download or read book Stochastic Approximations Via Large Deviations: Asymptotic Properties written by Paul Dupuis and published by . This book was released on 1984 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic properties of Robbins-Munro and Kiefer-Wolfowitz type stochastic approximation algorithms are obtained via the theory of large deviations. The conditions are weak and can even yield w.p.l. convergence results. The probability of escape of the iterates from a neighborhood of a stable point of the algorithm is estimated and shown to be considerably smaller than suggested by the classical asymptotic normality of local normalized errors method of getting the asymptotic properties. The escape probabilities are a natural quantity of interest. In many applications, they are more useful than the local normalized mean square errors. Other large deviations estimates are also obtained. Keywords: Recursive algorithms.
Book Synopsis Asymptotic Behavior of Constrained Stochastic Approximations Via the Theory of Large Deviations by : Paul Dupuis
Download or read book Asymptotic Behavior of Constrained Stochastic Approximations Via the Theory of Large Deviations written by Paul Dupuis and published by . This book was released on 1985 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt: This document describes a projected recursive (or stochastic approximation) algorithm which arises frequently in applications in control and communications theory. There is a sizeable literature concerning its asymptotic properties as epsilon approaching limit of o with epsilon sub n approaching limit of t or epsilon n approaching infinity. Keywords: Convergence; Asymptotic normality.
Book Synopsis Asymptotic Behavior of Stochastic Approximation and Large Deviations by : Harold J. Kushner
Download or read book Asymptotic Behavior of Stochastic Approximation and Large Deviations written by Harold J. Kushner and published by . This book was released on 1983 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of large deviations is applied to the study of the asymptotic properties of the stochastic approximation algorithms. The method provides a useful alternative to the currently used technique of obtaining rate of convergence results.
Book Synopsis Stochastic Approximation and Optimization of Random Systems by : Lennart Ljung
Download or read book Stochastic Approximation and Optimization of Random Systems written by Lennart Ljung and published by Birkhauser. This book was released on 1992 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stochastic Approximation by : Cyrus Derman
Download or read book Stochastic Approximation written by Cyrus Derman and published by . This book was released on 1956 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Behavior of Stochastic Approximation and Large Deviations /by Harold J. Kushner by : Harold Joseph Kushner
Download or read book Asymptotic Behavior of Stochastic Approximation and Large Deviations /by Harold J. Kushner written by Harold Joseph Kushner and published by . This book was released on 1983 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stochastic Approximation by : M. T. Wasan
Download or read book Stochastic Approximation written by M. T. Wasan and published by Cambridge University Press. This book was released on 2004-06-03 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous mathematical treatment of the technique for studying the properties of an experimental situation.
Book Synopsis The Theory of Large Deviations and the Asymptotic Analysis of Recursive Algorithms and Stochastic Approximation by : Harold J. Kushner
Download or read book The Theory of Large Deviations and the Asymptotic Analysis of Recursive Algorithms and Stochastic Approximation written by Harold J. Kushner and published by . This book was released on 1984 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Approximations of Stochastic Maxwell Equations by : Chuchu Chen
Download or read book Numerical Approximations of Stochastic Maxwell Equations written by Chuchu Chen and published by Springer Nature. This book was released on 2024-01-04 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: The stochastic Maxwell equations play an essential role in many fields, including fluctuational electrodynamics, statistical radiophysics, integrated circuits, and stochastic inverse problems. This book provides some recent advances in the investigation of numerical approximations of the stochastic Maxwell equations via structure-preserving algorithms. It presents an accessible overview of the construction and analysis of structure-preserving algorithms with an emphasis on the preservation of geometric structures, physical properties, and asymptotic behaviors of the stochastic Maxwell equations. A friendly introduction to the simulation of the stochastic Maxwell equations with some structure-preserving algorithms is provided using MATLAB for the reader’s convenience. The objects considered in this book are related to several fascinating mathematical fields: numerical analysis, stochastic analysis, (multi-)symplectic geometry, large deviations principle, ergodic theory, partial differential equation, probability theory, etc. This book will appeal to researchers who are interested in these topics.
Book Synopsis Two-Scale Stochastic Systems by : Yuri Kabanov
Download or read book Two-Scale Stochastic Systems written by Yuri Kabanov and published by Springer Science & Business Media. This book was released on 2003 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two-scale systems described by singularly perturbed SDEs have been the subject of ample literature. However, this new monograph develops subjects that were rarely addressed and could be given the collective description "Stochastic Tikhonov-Levinson theory and its applications." The book provides a mathematical apparatus designed to analyze the dynamic behaviour of a randomly perturbed system with fast and slow variables. In contrast to the deterministic Tikhonov-Levinson theory, the basic model is described in a more realistic way by stochastic differential equations. This leads to a number of new theoretical questions but simultaneously allows us to treat in a unified way a surprisingly wide spectrum of applications like fast modulations, approximate filtering, and stochastic approximation.Two-scale systems described by singularly perturbed SDEs have been the subject of ample literature. However, this new monograph develops subjects that were rarely addressed and could be given the collective description "Stochastic Tikhonov-Levinson theory and its applications." The book provides a mathematical apparatus designed to analyze the dynamic behaviour of a randomly perturbed system with fast and slow variables. In contrast to the deterministic Tikhonov-Levinson theory, the basic model is described in a more realistic way by stochastic differential equations. This leads to a number of new theoretical questions but simultaneously allows us to treat in a unified way a surprisingly wide spectrum of applications like fast modulations, approximate filtering, and stochastic approximation.
Book Synopsis Stochastic Approximation and Recursive Algorithms and Applications by : Harold Kushner
Download or read book Stochastic Approximation and Recursive Algorithms and Applications written by Harold Kushner and published by Springer. This book was released on 1997-06-12 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most comprehensive and thorough treatment of modern stochastic approximation type algorithms to date, based on powerful methods connected with that of the ODE. It covers general constrained and unconstrained problems, w.p.1 as well as the very successful weak convergence methods under weak conditions on the dynamics and noise processes, asymptotic properties and rates of convergence, iterate averaging methods, ergodic cost problems, state dependent noise, high dimensional problems, plus decentralized and asynchronous algorithms, and the use of methods of large deviations. Examples from many fields illustrate and motivate the techniques.
Book Synopsis Large Deviations for Stochastic Processes by : Jin Feng
Download or read book Large Deviations for Stochastic Processes written by Jin Feng and published by American Mathematical Soc.. This book was released on 2015-02-03 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the results on large deviations for a class of stochastic processes. Following an introduction and overview, the material is presented in three parts. Part 1 gives necessary and sufficient conditions for exponential tightness that are analogous to conditions for tightness in the theory of weak convergence. Part 2 focuses on Markov processes in metric spaces. For a sequence of such processes, convergence of Fleming's logarithmically transformed nonlinear semigroups is shown to imply the large deviation principle in a manner analogous to the use of convergence of linear semigroups in weak convergence. Viscosity solution methods provide applicable conditions for the necessary convergence. Part 3 discusses methods for verifying the comparison principle for viscosity solutions and applies the general theory to obtain a variety of new and known results on large deviations for Markov processes. In examples concerning infinite dimensional state spaces, new comparison principles are derived for a class of Hamilton-Jacobi equations in Hilbert spaces and in spaces of probability measures.
Book Synopsis Stochastic Approximation and Large Deviations by : P. Dupuis
Download or read book Stochastic Approximation and Large Deviations written by P. Dupuis and published by . This book was released on 1988 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Properties of Decentralized Stochastic Approximation Algorithms by : Gang Yin
Download or read book Asymptotic Properties of Decentralized Stochastic Approximation Algorithms written by Gang Yin and published by . This book was released on 1987 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Analysis and Approximation of Rare Events by : Amarjit Budhiraja
Download or read book Analysis and Approximation of Rare Events written by Amarjit Budhiraja and published by Springer. This book was released on 2019-08-10 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents broadly applicable methods for the large deviation and moderate deviation analysis of discrete and continuous time stochastic systems. A feature of the book is the systematic use of variational representations for quantities of interest such as normalized logarithms of probabilities and expected values. By characterizing a large deviation principle in terms of Laplace asymptotics, one converts the proof of large deviation limits into the convergence of variational representations. These features are illustrated though their application to a broad range of discrete and continuous time models, including stochastic partial differential equations, processes with discontinuous statistics, occupancy models, and many others. The tools used in the large deviation analysis also turn out to be useful in understanding Monte Carlo schemes for the numerical approximation of the same probabilities and expected values. This connection is illustrated through the design and analysis of importance sampling and splitting schemes for rare event estimation. The book assumes a solid background in weak convergence of probability measures and stochastic analysis, and is suitable for advanced graduate students, postdocs and researchers.
Book Synopsis Asymptotic Properties of Distributed and Communicating Stochastic Approximation Algorithms by : Harold Joseph Kushner
Download or read book Asymptotic Properties of Distributed and Communicating Stochastic Approximation Algorithms written by Harold Joseph Kushner and published by . This book was released on 1986 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: The asymptotic properties of extensions of the type of distributed or decentralized stochastic approximation proposed are developed. Such algorithms have numerous potential applications in decentralized estimation, detection and adaptive control, or in decentralized Monte Carlo simulation for system optimization (where they can exploit th possibilities of parallel processing). The structure involves several isolated processors (recursive algorithms) who communicate to each other asyhnchronously and at random intervals. The asymptotic (small gain) properties are derived. The communication intervals need not be strictly bounded and they and the system noise can depend on the (communicating) system state. State space constraints are also handled. In many applications, the dynamical terms are merely indicator functions, or have other types of discontinuities. The typical such case is also treated, as is the case where there is noise in the communication. The linear stochastic differential equation satisfied by the (interpolated) asymptotic normalized error sequence is derived, and issued to compare alternative algorithms and communication strategies. Weak convergence methods provide the basic tools.
Book Synopsis Stochastic Approximation and Recursive Algorithms and Applications by : Harold Kushner
Download or read book Stochastic Approximation and Recursive Algorithms and Applications written by Harold Kushner and published by Springer Science & Business Media. This book was released on 2006-05-04 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a thorough development of the modern theory of stochastic approximation or recursive stochastic algorithms for both constrained and unconstrained problems. This second edition is a thorough revision, although the main features and structure remain unchanged. It contains many additional applications and results as well as more detailed discussion.
