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General Convergence Results For Stochastic Approximations Via Weak Convergence Theory
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Book Synopsis General Convergence Results for Stochastic Approximations Via Weak Convergence Theory by : Harold J. Kushner
Download or read book General Convergence Results for Stochastic Approximations Via Weak Convergence Theory written by Harold J. Kushner and published by . This book was released on 1976 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using results in the theory of weak convergence of measures and in stability theory for ordinary differential equations, we prove some general convergence theorems for the sequences of random variables which are generated by algorithms of the stochastic approximation type. Such algorithms are used when one wishes to locate, via a recursive Monte-Carlo method, a minimum of a function, under handicap of noisy data. Algorithms for both constrained and unconstrained optimization problems will be considered, and for rather general noise processes. (Author).
Book Synopsis Approximation and Weak Convergence Methods for Random Processes, with Applications to Stochastic Systems Theory by : Harold Joseph Kushner
Download or read book Approximation and Weak Convergence Methods for Random Processes, with Applications to Stochastic Systems Theory written by Harold Joseph Kushner and published by MIT Press. This book was released on 1984 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Control and communications engineers, physicists, and probability theorists, among others, will find this book unique. It contains a detailed development of approximation and limit theorems and methods for random processes and applies them to numerous problems of practical importance. In particular, it develops usable and broad conditions and techniques for showing that a sequence of processes converges to a Markov diffusion or jump process. This is useful when the natural physical model is quite complex, in which case a simpler approximation la diffusion process, for example) is usually made. The book simplifies and extends some important older methods and develops some powerful new ones applicable to a wide variety of limit and approximation problems. The theory of weak convergence of probability measures is introduced along with general and usable methods (for example, perturbed test function, martingale, and direct averaging) for proving tightness and weak convergence. Kushner's study begins with a systematic development of the method. It then treats dynamical system models that have state-dependent noise or nonsmooth dynamics. Perturbed Liapunov function methods are developed for stability studies of nonMarkovian problems and for the study of asymptotic distributions of non-Markovian systems. Three chapters are devoted to applications in control and communication theory (for example, phase-locked loops and adoptive filters). Smallnoise problems and an introduction to the theory of large deviations and applications conclude the book. Harold J. Kushner is Professor of Applied Mathematics and Engineering at Brown University and is one of the leading researchers in the area of stochastic processes concerned with analysis and synthesis in control and communications theory. This book is the sixth in The MIT Press Series in Signal Processing, Optimization, and Control, edited by Alan S. Willsky.
Book Synopsis I, II Convergence and Rate of Convergence Theorems for Constrained and Unconstrained Stochastic Approximation, Via Weak Convergence Methods. III Numerical Studies for Constrained Stochastic Approximation Problems by : Harold J. Kushner
Download or read book I, II Convergence and Rate of Convergence Theorems for Constrained and Unconstrained Stochastic Approximation, Via Weak Convergence Methods. III Numerical Studies for Constrained Stochastic Approximation Problems written by Harold J. Kushner and published by . This book was released on 1976 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This report contains 3 papers. The first two deal with applications of the theory of weak convergence to general results in constrained and unconstrained stochastic approximation. The third paper gives an extensive discussion of the numerical properties of four algorithms for the constrained case.
Book Synopsis Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems by : Harold Kushner
Download or read book Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems written by Harold Kushner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with several closely related topics concerning approxima tions and perturbations of random processes and their applications to some important and fascinating classes of problems in the analysis and design of stochastic control systems and nonlinear filters. The basic mathematical methods which are used and developed are those of the theory of weak con vergence. The techniques are quite powerful for getting weak convergence or functional limit theorems for broad classes of problems and many of the techniques are new. The original need for some of the techniques which are developed here arose in connection with our study of the particular applica tions in this book, and related problems of approximation in control theory, but it will be clear that they have numerous applications elsewhere in weak convergence and process approximation theory. The book is a continuation of the author's long term interest in problems of the approximation of stochastic processes and its applications to problems arising in control and communication theory and related areas. In fact, the techniques used here can be fruitfully applied to many other areas. The basic random processes of interest can be described by solutions to either (multiple time scale) Ito differential equations driven by wide band or state dependent wide band noise or which are singularly perturbed. They might be controlled or not, and their state values might be fully observable or not (e. g. , as in the nonlinear filtering problem).
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 2013-11-11 with total page 432 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 Convergence of Recursive Adaptive and Identification Procedures Via Weak Convergence Theory by : Harold J. Kushner
Download or read book Convergence of Recursive Adaptive and Identification Procedures Via Weak Convergence Theory written by Harold J. Kushner and published by . This book was released on 1976 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results and concepts in the theory of weak convergence of a sequence of probability measures are applied to convergence problems for a variety of recursive adaptive (stochastic approximation like) methods. Similar techniques have had wide applicability in areas of operations research and in some other areas in stochastic control. It is quite likely that they will play a much more important role in control theory than they do at present, since they allow relatively simple and natural proofs for many types of convergence and approximation problems. Part of the aim of the paper is tutorial: to introduce the ideas, and to show how they might be applied. Also, many of the results are new, and they can all be generalized in many directions. (Author).
Book Synopsis Stochastic Approximation Methods for Constrained and Unconstrained Systems by : H.J. Kushner
Download or read book Stochastic Approximation Methods for Constrained and Unconstrained Systems written by H.J. Kushner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with a powerful and convenient approach to a great variety of types of problems of the recursive monte-carlo or stochastic approximation type. Such recu- sive algorithms occur frequently in stochastic and adaptive control and optimization theory and in statistical esti- tion theory. Typically, a sequence {X } of estimates of a n parameter is obtained by means of some recursive statistical th st procedure. The n estimate is some function of the n_l estimate and of some new observational data, and the aim is to study the convergence, rate of convergence, and the pa- metric dependence and other qualitative properties of the - gorithms. In this sense, the theory is a statistical version of recursive numerical analysis. The approach taken involves the use of relatively simple compactness methods. Most standard results for Kiefer-Wolfowitz and Robbins-Monro like methods are extended considerably. Constrained and unconstrained problems are treated, as is the rate of convergence problem. While the basic method is rather simple, it can be elaborated to allow a broad and deep coverage of stochastic approximation like problems. The approach, relating algorithm behavior to qualitative properties of deterministic or stochastic differ ential equations, has advantages in algorithm conceptualiza tion and design. It is often possible to obtain an intuitive understanding of algorithm behavior or qualitative dependence upon parameters, etc., without getting involved in a great deal of deta~l.
Book Synopsis Convergence of Stochastic Processes by : D. Pollard
Download or read book Convergence of Stochastic Processes written by D. Pollard and published by David Pollard. This book was released on 1984-10-08 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functionals on stochastic processes; Uniform convergence of empirical measures; Convergence in distribution in euclidean spaces; Convergence in distribution in metric spaces; The uniform metric on space of cadlag functions; The skorohod metric on D [0, oo); Central limit teorems; Martingales.
Book Synopsis Weak Convergence and Its Applications by : Zhengyan Lin
Download or read book Weak Convergence and Its Applications written by Zhengyan Lin and published by World Scientific. This book was released on 2014 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Weak convergence of stochastic processes is one of most important theories in probability theory. Not only probability experts but also more and more statisticians are interested in it. In the study of statistics and econometrics, some problems cannot be solved by the classical method. In this book, we will introduce some recent development of modern weak convergence theory to overcome defects of classical theory.Contents: "The Definition and Basic Properties of Weak Convergence: "Metric SpaceThe Definition of Weak Convergence of Stochastic Processes and Portmanteau TheoremHow to Verify the Weak Convergence?Two Examples of Applications of Weak Convergence"Convergence to the Independent Increment Processes: "The Basic Conditions of Convergence to the Gaussian Independent Increment ProcessesDonsker Invariance PrincipleConvergence of Poisson Point ProcessesTwo Examples of Applications of Point Process Method"Convergence to Semimartingales: "The Conditions of Tightness for Semimartingale SequenceWeak Convergence to SemimartingaleWeak Convergence to Stochastic Integral I: The Martingale Convergence ApproachWeak Convergence to Stochastic Integral II: Kurtz and Protter's ApproachStable Central Limit Theorem for SemimartingalesAn Application to Stochastic Differential EquationsAppendix: The Predictable Characteristics of Semimartingales"Convergence of Empirical Processes: "Classical Weak Convergence of Empirical ProcessesWeak Convergence of Marked Empirical ProcessesWeak Convergence of Function Index Empirical ProcessesWeak Convergence of Empirical Processes Involving Time-Dependent dataTwo Examples of Applications in Statistics Readership: Graduate students and researchers in probability & statistics and econometrics.
Book Synopsis Weak Convergence of Stochastic Approximation Processes with Random Indices by : Edward W. Frees
Download or read book Weak Convergence of Stochastic Approximation Processes with Random Indices written by Edward W. Frees and published by . This book was released on 1983 with total page 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 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 Stochastic Approximation and Large Deviations: General Results for W.p.l. Convergence by : Paul Gilbert Dupuis
Download or read book Stochastic Approximation and Large Deviations: General Results for W.p.l. Convergence written by Paul Gilbert Dupuis and published by . This book was released on 1987 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: W.p.l. convergence results are obtained for stochastic recursive approximation algorithms under very general conditions. The gain sequence (a sub n) can go to zero very slowly and state-dependent noise, discontinuous dynamical equations and the projected or constrained algorithm are all treated. The basic technique is the theory of large deviations. Prior results obtained via this theory are extended in many directions. Keywords: Local linearization; Errors for tracking systems.
Book Synopsis Adaptive Filtering Prediction and Control by : Graham C Goodwin
Download or read book Adaptive Filtering Prediction and Control written by Graham C Goodwin and published by Courier Corporation. This book was released on 2014-05-05 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unified survey focuses on linear discrete-time systems and explores natural extensions to nonlinear systems. It emphasizes discrete-time systems, summarizing theoretical and practical aspects of a large class of adaptive algorithms. 1984 edition.
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 1992 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Learning Algorithms Theory and Applications by : S. Lakshmivarahan
Download or read book Learning Algorithms Theory and Applications written by S. Lakshmivarahan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learning constitutes one of the most important phase of the whole psychological processes and it is essential in many ways for the occurrence of necessary changes in the behavior of adjusting organisms. In a broad sense influence of prior behavior and its consequence upon subsequent behavior is usually accepted as a definition of learning. Till recently learning was regarded as the prerogative of living beings. But in the past few decades there have been attempts to construct learning machines or systems with considerable success. This book deals with a powerful class of learning algorithms that have been developed over the past two decades in the context of learning systems modelled by finite state probabilistic automaton. These algorithms are very simple iterative schemes. Mathematically these algorithms define two distinct classes of Markov processes with unit simplex (of suitable dimension) as its state space. The basic problem of learning is viewed as one of finding conditions on the algorithm such that the associated Markov process has prespecified asymptotic behavior. As a prerequisite a first course in analysis and stochastic processes would be an adequate preparation to pursue the development in various chapters.
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:
