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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 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.
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 and Optimization of Random Systems by : L. Ljung
Download or read book Stochastic Approximation and Optimization of Random Systems written by L. Ljung and published by Birkhäuser. This book was released on 2012-12-06 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The DMV seminar "Stochastische Approximation und Optimierung zufalliger Systeme" was held at Blaubeuren, 28. 5. -4. 6. 1989. The goal was to give an approach to theory and application of stochas tic approximation in view of optimization problems, especially in engineering systems. These notes are based on the seminar lectures. They consist of three parts: I. Foundations of stochastic approximation (H. Walk); n. Applicational aspects of stochastic approximation (G. PHug); In. Applications to adaptation :ugorithms (L. Ljung). The prerequisites for reading this book are basic knowledge in probability, mathematical statistics, optimization. We would like to thank Prof. M. Barner and Prof. G. Fischer for the or ganization of the seminar. We also thank the participants for their cooperation and our assistants and secretaries for typing the manuscript. November 1991 L. Ljung, G. PHug, H. Walk Table of contents I Foundations of stochastic approximation (H. Walk) §1 Almost sure convergence of stochastic approximation procedures 2 §2 Recursive methods for linear problems 17 §3 Stochastic optimization under stochastic constraints 22 §4 A learning model; recursive density estimation 27 §5 Invariance principles in stochastic approximation 30 §6 On the theory of large deviations 43 References for Part I 45 11 Applicational aspects of stochastic approximation (G. PHug) §7 Markovian stochastic optimization and stochastic approximation procedures 53 §8 Asymptotic distributions 71 §9 Stopping times 79 §1O Applications of stochastic approximation methods 80 References for Part II 90 III Applications to adaptation algorithms (L.
Book Synopsis Large Deviations For Performance Analysis by : Alan Weiss
Download or read book Large Deviations For Performance Analysis written by Alan Weiss and published by Routledge. This book was released on 2019-03-07 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1995, Large Deviations for Performance Analysis consists of two synergistic parts. The first half develops the theory of large deviations from the beginning, through recent results on the theory for processes with boundaries, keeping to a very narrow path: continuous-time, discrete-state processes. By developing only what is needed for the applications, the theory is kept to a manageable level, both in terms of length and in terms of difficulty. Within its scope, the treatment is detailed, comprehensive and self-contained. As the book shows, there are sufficiently many interesting applications of jump Markov processes to warrant a special treatment. The second half is a collection of applications developed at Bell Laboratories. The applications cover large areas of the theory of communication networks: circuit switched transmission, packet transmission, multiple access channels, and the M/M/1 queue. Aspects of parallel computation are covered as well including, basics of job allocation, rollback-based parallel simulation, assorted priority queueing models that might be used in performance models of various computer architectures, and asymptotic coupling of processors. These applications are thoroughly analysed using the tools developed in the first half of the book.
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 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 Adaptive Statistical Procedures and Related Topics by : John Van Ryzin
Download or read book Adaptive Statistical Procedures and Related Topics written by John Van Ryzin and published by IMS. This book was released on 1986 with total page 496 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 The Conquest of American Inflation by : Thomas J. Sargent
Download or read book The Conquest of American Inflation written by Thomas J. Sargent and published by Princeton University Press. This book was released on 2018-06-05 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past fifteen years, inflation has been conquered by many advanced countries. History reveals, however, that it has been conquered before and returned. In The Conquest of American Inflation, Thomas J. Sargent presents a groundbreaking analysis of the rise and fall of U.S. inflation after 1960. He examines two broad explanations for the behavior of inflation and unemployment in this period: the natural-rate hypothesis joined to the Lucas critique and a more traditional econometric policy evaluation modified to include adaptive expectations and learning. His purpose is not only to determine which is the better account, but also to codify for the benefit of the next generation the economic forces that cause inflation. Sargent begins with an explanation of how American policymakers increased inflation in the early 1960s by following erroneous assumptions about the exploitability of the Phillips curve--the inverse relationship between inflation and unemployment. In subsequent chapters, he connects a sequence of ideas--self-confirming equilibria, least-squares and other adaptive or recursive learning algorithms, convergence of least-squares learners with self-confirming equilibria, and recurrent dynamics along escape routes from self-confirming equilibria. Sargent synthesizes results from macroeconomics, game theory, control theory, and other fields to extend both adaptive expectations and rational expectations theory, and he compellingly describes postwar inflation in terms of drifting coefficients. He interprets his results in favor of adaptive expectations as the relevant mechanism affecting inflation policy. Providing an original methodological link between theoretical and policy economics, this book will engender much debate and become an indispensable text for academics, graduate students, and professional economists.
Book Synopsis SIAM Journal on Control and Optimization by : Society for Industrial and Applied Mathematics
Download or read book SIAM Journal on Control and Optimization written by Society for Industrial and Applied Mathematics and published by . This book was released on 2002 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Behaviour of Linearly Transformed Sums of Random Variables by : V.V. Buldygin
Download or read book Asymptotic Behaviour of Linearly Transformed Sums of Random Variables written by V.V. Buldygin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Limit theorems for random sequences may conventionally be divided into two large parts, one of them dealing with convergence of distributions (weak limit theorems) and the other, with almost sure convergence, that is to say, with asymptotic prop erties of almost all sample paths of the sequences involved (strong limit theorems). Although either of these directions is closely related to another one, each of them has its own range of specific problems, as well as the own methodology for solving the underlying problems. This book is devoted to the second of the above mentioned lines, which means that we study asymptotic behaviour of almost all sample paths of linearly transformed sums of independent random variables, vectors, and elements taking values in topological vector spaces. In the classical works of P.Levy, A.Ya.Khintchine, A.N.Kolmogorov, P.Hartman, A.Wintner, W.Feller, Yu.V.Prokhorov, and M.Loeve, the theory of almost sure asymptotic behaviour of increasing scalar-normed sums of independent random vari ables was constructed. This theory not only provides conditions of the almost sure convergence of series of independent random variables, but also studies different ver sions of the strong law of large numbers and the law of the iterated logarithm. One should point out that, even in this traditional framework, there are still problems which remain open, while many definitive results have been obtained quite recently.
Book Synopsis System Identification Using Regular and Quantized Observations by : Qi He
Download or read book System Identification Using Regular and Quantized Observations written by Qi He and published by Springer Science & Business Media. This book was released on 2013-02-11 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief presents characterizations of identification errors under a probabilistic framework when output sensors are binary, quantized, or regular. By considering both space complexity in terms of signal quantization and time complexity with respect to data window sizes, this study provides a new perspective to understand the fundamental relationship between probabilistic errors and resources, which may represent data sizes in computer usage, computational complexity in algorithms, sample sizes in statistical analysis and channel bandwidths in communications.
Book Synopsis Proceedings of the 26th IEEE Conference on Decision and Control by :
Download or read book Proceedings of the 26th IEEE Conference on Decision and Control written by and published by . This book was released on 1987 with total page 930 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on with total page 1050 pages. Available in PDF, EPUB and Kindle. Book excerpt:
