Introduction To Stochastic Processes

Introduction To Stochastic Processes
Author :
Publisher : World Scientific
Total Pages : 245
Release :
ISBN-10 : 9789814740326
ISBN-13 : 9814740322
Rating : 4/5 (322 Downloads)

Book Synopsis Introduction To Stochastic Processes by : Mu-fa Chen

Download or read book Introduction To Stochastic Processes written by Mu-fa Chen and published by World Scientific. This book was released on 2021-05-25 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of this book is to introduce the elements of stochastic processes in a rather concise manner where we present the two most important parts — Markov chains and stochastic analysis. The readers are led directly to the core of the main topics to be treated in the context. Further details and additional materials are left to a section containing abundant exercises for further reading and studying.In the part on Markov chains, the focus is on the ergodicity. By using the minimal nonnegative solution method, we deal with the recurrence and various types of ergodicity. This is done step by step, from finite state spaces to denumerable state spaces, and from discrete time to continuous time. The methods of proofs adopt modern techniques, such as coupling and duality methods. Some very new results are included, such as the estimate of the spectral gap. The structure and proofs in the first part are rather different from other existing textbooks on Markov chains.In the part on stochastic analysis, we cover the martingale theory and Brownian motions, the stochastic integral and stochastic differential equations with emphasis on one dimension, and the multidimensional stochastic integral and stochastic equation based on semimartingales. We introduce three important topics here: the Feynman-Kac formula, random time transform and Girsanov transform. As an essential application of the probability theory in classical mathematics, we also deal with the famous Brunn-Minkowski inequality in convex geometry.This book also features modern probability theory that is used in different fields, such as MCMC, or even deterministic areas: convex geometry and number theory. It provides a new and direct routine for students going through the classical Markov chains to the modern stochastic analysis.


Introduction To Stochastic Processes Related Books

Stochastic Processes
Language: en
Pages: 356
Authors: Narahari Umanath Prabhu
Categories: Mathematics
Type: BOOK - Published: 2007 - Publisher: World Scientific

DOWNLOAD EBOOK

Most introductory textbooks on stochastic processes which cover standard topics such as Poisson process, Brownian motion, renewal theory and random walks deal i
Basics of Applied Stochastic Processes
Language: en
Pages: 452
Authors: Richard Serfozo
Categories: Mathematics
Type: BOOK - Published: 2009-01-24 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

Stochastic processes are mathematical models of random phenomena that evolve according to prescribed dynamics. Processes commonly used in applications are Marko
Introduction to Stochastic Processes
Language: en
Pages: 280
Authors: Mu-Fa Chen
Categories: Mathematics
Type: BOOK - Published: 2021 - Publisher: Wspc/Hep

DOWNLOAD EBOOK

The objective here is to introduce the elements of stochastic processes in a rather concise manner where we present the two most important parts in stochastic p
An Introduction to Stochastic Processes and Their Applications
Language: en
Pages: 302
Authors: Petar Todorovic
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

This text on stochastic processes and their applications is based on a set of lectures given during the past several years at the University of California, Sant
Theory and Applications of Stochastic Processes
Language: en
Pages: 486
Authors: Zeev Schuss
Categories: Mathematics
Type: BOOK - Published: 2009-12-09 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

Stochastic processes and diffusion theory are the mathematical underpinnings of many scientific disciplines, including statistical physics, physical chemistry,