Real Analysis Methods For Markov Processes

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Real Analysis Methods For Markov Processes

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Author : Kazuaki Taira
language : en
Publisher: Springer Nature
Release Date : 2024

Real Analysis Methods For Markov Processes written by Kazuaki Taira and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with Boundary value problems categories.

Zusammenfassung: This book is devoted to real analysis methods for the problem of constructing Markov processes with boundary conditions in probability theory. Analytically, a Markovian particle in a domain of Euclidean space is governed by an integro-differential operator, called the Waldenfels operator, in the interior of the domain, and it obeys a boundary condition, called the Ventcel (Wentzell) boundary condition, on the boundary of the domain. Most likely, a Markovian particle moves both by continuous paths and by jumps in the state space and obeys the Ventcel boundary condition, which consists of six terms corresponding to diffusion along the boundary, an absorption phenomenon, a reflection phenomenon, a sticking (or viscosity) phenomenon, and a jump phenomenon on the boundary and an inward jump phenomenon from the boundary. More precisely, we study a class of first-order Ventcel boundary value problems for second-order elliptic Waldenfels integro-differential operators. By using the Calderón-Zygmund theory of singular integrals, we prove the existence and uniqueness of theorems in the framework of the Sobolev and Besov spaces, which extend earlier theorems due to Bony-Courrège-Priouret to the vanishing mean oscillation (VMO) case. Our proof is based on various maximum principles for second-order elliptic differential operators with discontinuous coefficients in the framework of Sobolev spaces. My approach is distinguished by the extensive use of the ideas and techniques characteristic of recent developments in the theory of singular integral operators due to Calderón and Zygmund. Moreover, we make use of an Lp variant of an estimate for the Green operator of the Neumann problem introduced in the study of Feller semigroups by me. The present book is amply illustrated; 119 figures and 12 tables are provided in such a fashion that a broad spectrum of readers understand our problem and main results

Analytical Methods For Kolmogorov Equations

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Author : Luca Lorenzi
language : en
Publisher: CRC Press
Release Date : 2016-10-04

Analytical Methods For Kolmogorov Equations written by Luca Lorenzi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-04 with Mathematics categories.

The second edition of this book has a new title that more accurately reflects the table of contents. Over the past few years, many new results have been proven in the field of partial differential equations. This edition takes those new results into account, in particular the study of nonautonomous operators with unbounded coefficients, which has received great attention. Additionally, this edition is the first to use a unified approach to contain the new results in a singular place.

Lectures On The Coupling Method

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Author : Torgny Lindvall
language : en
Publisher: Courier Corporation
Release Date : 2012-08-15

Lectures On The Coupling Method written by Torgny Lindvall and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-15 with Mathematics categories.

Practical and easy-to-use reference progresses from simple to advanced topics, covering, among other topics, renewal theory, Markov chains, Poisson approximation, ergodicity, and Strassen's theorem. 1992 edition.

Ergodic Behavior Of Markov Processes

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Author : Alexei Kulik
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-11-20

Ergodic Behavior Of Markov Processes written by Alexei Kulik 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 2017-11-20 with Mathematics categories.

The general topic of this book is the ergodic behavior of Markov processes. A detailed introduction to methods for proving ergodicity and upper bounds for ergodic rates is presented in the first part of the book, with the focus put on weak ergodic rates, typical for Markov systems with complicated structure. The second part is devoted to the application of these methods to limit theorems for functionals of Markov processes. The book is aimed at a wide audience with a background in probability and measure theory. Some knowledge of stochastic processes and stochastic differential equations helps in a deeper understanding of specific examples. Contents Part I: Ergodic Rates for Markov Chains and Processes Markov Chains with Discrete State Spaces General Markov Chains: Ergodicity in Total Variation MarkovProcesseswithContinuousTime Weak Ergodic Rates Part II: Limit Theorems The Law of Large Numbers and the Central Limit Theorem Functional Limit Theorems

Markov Processes Gaussian Processes And Local Times

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Author : Michael B. Marcus
language : en
Publisher: Cambridge University Press
Release Date : 2006-07-24

Markov Processes Gaussian Processes And Local Times written by Michael B. Marcus and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-24 with Mathematics categories.

A readable 2006 synthesis of three main areas in the modern theory of stochastic processes.

Approximate Iterative Algorithms

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Author : Anthony Louis Almudevar
language : en
Publisher: CRC Press
Release Date : 2014-02-18

Approximate Iterative Algorithms written by Anthony Louis Almudevar and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-18 with Computers categories.

Iterative algorithms often rely on approximate evaluation techniques, which may include statistical estimation, computer simulation or functional approximation. This volume presents methods for the study of approximate iterative algorithms, providing tools for the derivation of error bounds and convergence rates, and for the optimal design of such

Theory Of Stochastic Processes

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Author : Dmytro Gusak
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-10

Theory Of Stochastic Processes written by Dmytro Gusak 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 2010-07-10 with Mathematics categories.

Providing the necessary materials within a theoretical framework, this volume presents stochastic principles and processes, and related areas. Over 1000 exercises illustrate the concepts discussed, including modern approaches to sample paths and optimal stopping.

Guide To Programs

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Author : National Science Foundation (U.S.)
language : en
Publisher:
Release Date : 1997

Guide To Programs written by National Science Foundation (U.S.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Federal aid to research categories.

An Introduction To Continuous Time Stochastic Processes

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Author : Vincenzo Capasso
language : en
Publisher: Springer Nature
Release Date : 2021-06-18

An Introduction To Continuous Time Stochastic Processes written by Vincenzo Capasso and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-18 with Mathematics categories.

This textbook, now in its fourth edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, it features concrete examples of modeling real-world problems from biology, medicine, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Unlike other books on stochastic methods that specialize in a specific field of applications, this volume examines the ways in which similar stochastic methods can be applied across different fields. Beginning with the fundamentals of probability, the authors go on to introduce the theory of stochastic processes, the Itô Integral, and stochastic differential equations. The following chapters then explore stability, stationarity, and ergodicity. The second half of the book is dedicated to applications to a variety of fields, including finance, biology, and medicine. Some highlights of this fourth edition include a more rigorous introduction to Gaussian white noise, additional material on the stability of stochastic semigroups used in models of population dynamics and epidemic systems, and the expansion of methods of analysis of one-dimensional stochastic differential equations. An Introduction to Continuous-Time Stochastic Processes, Fourth Edition is intended for graduate students taking an introductory course on stochastic processes, applied probability, stochastic calculus, mathematical finance, or mathematical biology. Prerequisites include knowledge of calculus and some analysis; exposure to probability would be helpful but not required since the necessary fundamentals of measure and integration are provided. Researchers and practitioners in mathematical finance, biomathematics, biotechnology, and engineering will also find this volume to be of interest, particularly the applications explored in the second half of the book.

Applied Probability And Stochastic Processes

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Author : J. George Shanthikumar
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Applied Probability And Stochastic Processes written by J. George Shanthikumar 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.

Applied Probability and Stochastic Processes is an edited work written in honor of Julien Keilson. This volume has attracted a host of scholars in applied probability, who have made major contributions to the field, and have written survey and state-of-the-art papers on a variety of applied probability topics, including, but not limited to: perturbation method, time reversible Markov chains, Poisson processes, Brownian techniques, Bayesian probability, optimal quality control, Markov decision processes, random matrices, queueing theory and a variety of applications of stochastic processes. The book has a mixture of theoretical, algorithmic, and application chapters providing examples of the cutting-edge work that Professor Keilson has done or influenced over the course of his highly-productive and energetic career in applied probability and stochastic processes. The book will be of interest to academic researchers, students, and industrial practitioners who seek to use the mathematics of applied probability in solving problems in modern society.