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Weak Convergence And Its Applications


Weak Convergence And Its Applications
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Weak Convergence And Its Applications


Weak Convergence And Its Applications
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Author : Zhengyan Lin
language : en
Publisher: World Scientific
Release Date : 2014

Weak Convergence And Its Applications written by Zhengyan Lin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Business & Economics categories.


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.



Weak Convergence Methods And Singularly Perturbed Stochastic Control And Filtering Problems


Weak Convergence Methods And Singularly Perturbed Stochastic Control And Filtering Problems
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Author : Harold Kushner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Weak Convergence Methods And Singularly Perturbed Stochastic Control And Filtering Problems written by Harold Kushner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.


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).



Weak Convergence Of Financial Markets


Weak Convergence Of Financial Markets
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Author : Jean-Luc Prigent
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Weak Convergence Of Financial Markets written by Jean-Luc Prigent and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Business & Economics categories.


A comprehensive overview of weak convergence of stochastic processes and its application to the study of financial markets. Split into three parts, the first recalls the mathematics of stochastic processes and stochastic calculus with special emphasis on contiguity properties and weak convergence of stochastic integrals. The second part is devoted to the analysis of financial theory from the convergence point of view. The main problems such as portfolio optimization, option pricing and hedging are examined, especially when considering discrete-time approximations of continuous-time dynamics. The third part deals with lattice- and tree-based computational procedures for option pricing both on stocks and stochastic bonds. More general discrete approximations are also introduced and detailed.



Empirical Processes With Applications To Statistics


Empirical Processes With Applications To Statistics
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Author : Galen R. Shorack
language : en
Publisher: SIAM
Release Date : 2009-09-24

Empirical Processes With Applications To Statistics written by Galen R. Shorack and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-24 with Mathematics categories.


Originally published in 1986, this valuable reference provides a detailed treatment of limit theorems and inequalities for empirical processes of real-valued random variables. It also includes applications of the theory to censored data, spacings, rank statistics, quantiles, and many functionals of empirical processes, including a treatment of bootstrap methods, and a summary of inequalities that are useful for proving limit theorems. At the end of the Errata section, the authors have supplied references to solutions for 11 of the 19 Open Questions provided in the book's original edition.



Weak Convergence And Its Applications


Weak Convergence And Its Applications
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Author : Zhengyan Lin
language : en
Publisher: World Scientific
Release Date : 2014-05-09

Weak Convergence And Its Applications written by Zhengyan Lin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-09 with Mathematics categories.


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.



Approximation And Weak Convergence Methods For Random Processes With Applications To Stochastic Systems Theory


Approximation And Weak Convergence Methods For Random Processes With Applications To Stochastic Systems Theory
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Author : Harold Joseph Kushner
language : en
Publisher: MIT Press
Release Date : 1984

Approximation And Weak Convergence Methods For Random Processes With Applications To Stochastic Systems Theory written by Harold Joseph Kushner and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Computers categories.


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.



Weak Convergence Of Measures


Weak Convergence Of Measures
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Author : Patrick Billingsley
language : en
Publisher: SIAM
Release Date : 1971-01-01

Weak Convergence Of Measures written by Patrick Billingsley and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971-01-01 with Mathematics categories.


A treatment of the convergence of probability measures from the foundations to applications in limit theory for dependent random variables. Mapping theorems are proved via Skorokhod's representation theorem; Prokhorov's theorem is proved by construction of a content. The limit theorems at the conclusion are proved under a new set of conditions that apply fairly broadly, but at the same time make possible relatively simple proofs.



Weak Convergence Of Stochastic Processes


Weak Convergence Of Stochastic Processes
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Author : Vidyadhar S. Mandrekar
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-09-26

Weak Convergence Of Stochastic Processes written by Vidyadhar S. Mandrekar and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-26 with Mathematics categories.


The purpose of this book is to present results on the subject of weak convergence in function spaces to study invariance principles in statistical applications to dependent random variables, U-statistics, censor data analysis. Different techniques, formerly available only in a broad range of literature, are for the first time presented here in a self-contained fashion. Contents: Weak convergence of stochastic processes Weak convergence in metric spaces Weak convergence on C[0, 1] and D[0,∞) Central limit theorem for semi-martingales and applications Central limit theorems for dependent random variables Empirical process Bibliography



Analysis And Approximation Of Rare Events


Analysis And Approximation Of Rare Events
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Author : Amarjit Budhiraja
language : en
Publisher: Springer
Release Date : 2019-08-10

Analysis And Approximation Of Rare Events written by Amarjit Budhiraja and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-10 with Mathematics categories.


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.



Principles Of Nonparametric Learning


Principles Of Nonparametric Learning
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Author : Laszlo Györfi
language : en
Publisher: Springer
Release Date : 2014-05-04

Principles Of Nonparametric Learning written by Laszlo Györfi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-04 with Technology & Engineering categories.


The book provides systematic in-depth analysis of nonparametric learning. It covers the theoretical limits and the asymptotical optimal algorithms and estimates, such as pattern recognition, nonparametric regression estimation, universal prediction, vector quantization, distribution and density estimation and genetic programming. The book is mainly addressed to postgraduates in engineering, mathematics, computer science, and researchers in universities and research institutions.