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An Introduction to Markov Processes (Graduate Texts in Mathematics) epub download

by Daniel W. Stroock


I bought this book not because I needed to learn about Markov processes (I deal with them rather often) but because I wanted a text that discussed time-inhomogeneous Markov processes, however briefly

I bought this book not because I needed to learn about Markov processes (I deal with them rather often) but because I wanted a text that discussed time-inhomogeneous Markov processes, however briefly. I have been told that Doob does this, but I can't ever seem to bring myself to put in the work necessary to really appreciate his stochastic processes book. Stroock gives a nice treatment of this topic in the context of simulated annealing, which is probably where most people would first encounter it these days.

An Introduction to Markov. has been added to your Cart

An Introduction to Markov. has been added to your Cart. The book provides a solid introduction into the study of stochastic processes and fills a significant gap in the literature: a text that provides a sophisticated study of stochastic processes in general (and Markov processes in particular) without a lot of heavy prerequisites. Stroock keeps the prerequisites very light.

Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag. The GTM series is easily identified by a white band at the top of the book.

This book provides a rigorous but elementary introduction to the theory of Markov Processes on a countable state space.

This book provides a rigorous but elementary introduction to the theory of Markov Processes on a countable . Applications are dispersed throughout the book. Topics covered are: Doeblin's theory, general ergodic properties, and continuous time processes. In addition, a whole chapter is devoted to reversible processes and the use of their associated Dirichlet forms to estimate the rate of convergence to equilibrium. Topics covered are: Doeblin's theory, general ergodic properties, and continuous time This book provides a rigorous but elementary introduction to the theory of Markov Processes on a countable state space.

Graduate Texts in Mathematics 1. TAKEUTI/ZARING

Graduate Texts in Mathematics 1. TAKEUTI/ZARING. Daniel W. Stroock MIT Department of Mathematics, Rm. 272 Massachusetts Ave 77 02139-4307 Cambridge, USA dws. Their book gives a no nonsense introduction to stochastic processes, especially Markov processes, on a countable state space, and its consistently honest, if not always easily assimilated, presentation of proofs is complemented by a daunting number of examples and exercises.

An abstract mathematical setting is given in which Markov processes are then defined and thoroughly studied

An abstract mathematical setting is given in which Markov processes are then defined and thoroughly studied. Because of this the book will basically be of interest to mathematicians and those who have at least a good knowledge of undergraduate analysis and probability theory. The proofs are clearly written and explanations are not too concise which makes this book indeed very useful for a graduate course.

Электронная книга "An Introduction to Markov Processes", Daniel W. Stroock

Электронная книга "An Introduction to Markov Processes", Daniel W. Stroock. Эту книгу можно прочитать в Google Play Книгах на компьютере, а также на устройствах Android и iOS. Выделяйте текст, добавляйте закладки и делайте заметки, скачав книгу "An Introduction to Markov Processes" для чтения в офлайн-режиме.

Provides a more accessible introduction than other books on Markov processes by emphasizing the structure of the subject and avoiding sophisticated measure theory

Leads the reader to a rigorous understanding of basic theory

An Introduction to Markov Processes (Graduate Texts in Mathematics) epub download

ISBN13: 978-3540234517

ISBN: 3540234519

Author: Daniel W. Stroock

Category: Math and Science

Subcategory: Mathematics

Language: English

Publisher: Springer; 2005 edition (May 31, 2005)

Pages: 178 pages

ePUB size: 1422 kb

FB2 size: 1272 kb

Rating: 4.9

Votes: 833

Other Formats: lit lrf txt docx

Related to An Introduction to Markov Processes (Graduate Texts in Mathematics) ePub books

Aradwyn
The book provides a solid introduction into the study of stochastic processes and fills a significant gap in the literature: a text that provides a sophisticated study of stochastic processes in general (and Markov processes in particular) without a lot of heavy prerequisites.

Stroock keeps the prerequisites very light. The reader need only have an understanding of some elementary topics. For undergraduate calculus, I recommend Apostle's two volume set Calculus, Vol. 1and Calculus,Vol. 2. Make sure you have a grasp of some basic matrix algebra, at least through eigenvectors and eigenvalues of a square matrix. You'll also need a good understanding of basic statistic/probability theory at the level of Hogg & Craig's Introduction to Mathematical Statistics, 6th Edition.

Stroock begins his book with a study of 1-dimensional random walks in Chapter 1. First passage times, first return times and the reflection principle are each introduced. (You'd study precisely the same topics from the Brownian motion point of view in an advanced measure-theoretic text). Higher dimensional random walks are introduced and transience/recurrence is studied.

A study of the Markov chain begins in earnest in Chapter 2. Stroock starts this chapter by establishing the existence of discrete time Markov chains using a construction technique based on a sequence of independent, identically distributed uniform random variables. This is a simple, yet powerful technique and different versions of this are used again in the construction of the Poisson process, the time homogenous Markov process, as well as the non-homogenous Markov process. Doeblin's Stationary Distribution Theorem is established and results from Ergodic Theory for these Doeblin chains are studied.

General (non-Doeblin) Markov chains are considered in Chapter 3. Stroock studies state communication and brings this together with some tools such as Doob's Stopping Time Theorem. Ergodic results are established in this context, starting with some simple results which are then refined.

Chapter 4 is a real highlight of the book. Continuous time Markov processes with values in a countable state space are studied in depth. This chapter focuses on the time-homogeneous case and starts with the construction of Poisson processes and compound Poisson processes. The Markov property is called out at each stage. These elementary stochastic processes are then used as the building blocks for the general time-homogenous Markov process (first with bounded, then unbounded transition rates). Ergodic Theory for these processes is then studied.

Chapter 5 builds towards a principle application, which is a Markov process study of simulated annealing. To get at this application, Stroock considers reversible Markov chains, reversible Markov processes, the Dirichlet form and Poincare's Inequality for this form. Gibbs states are studied next and the discussion of equilibriums leads quite naturally to both the study of simulated annealing and an extremely nice construction of a non-homogenous Markov process suited towards this study.

Chapter 6 is a primer for Lebesgue measure theory. Although this section is certainly not comprehensive, it is quite accessible, provides an interesting 'glimpse ahead' and suggests topics for further study.

Each chapter concludes with a number of really nice exercises of varying difficulty. The author is kind enough to provide some helpful hints for the more challenging problems.
Aradwyn
The book provides a solid introduction into the study of stochastic processes and fills a significant gap in the literature: a text that provides a sophisticated study of stochastic processes in general (and Markov processes in particular) without a lot of heavy prerequisites.

Stroock keeps the prerequisites very light. The reader need only have an understanding of some elementary topics. For undergraduate calculus, I recommend Apostle's two volume set Calculus, Vol. 1and Calculus,Vol. 2. Make sure you have a grasp of some basic matrix algebra, at least through eigenvectors and eigenvalues of a square matrix. You'll also need a good understanding of basic statistic/probability theory at the level of Hogg & Craig's Introduction to Mathematical Statistics, 6th Edition.

Stroock begins his book with a study of 1-dimensional random walks in Chapter 1. First passage times, first return times and the reflection principle are each introduced. (You'd study precisely the same topics from the Brownian motion point of view in an advanced measure-theoretic text). Higher dimensional random walks are introduced and transience/recurrence is studied.

A study of the Markov chain begins in earnest in Chapter 2. Stroock starts this chapter by establishing the existence of discrete time Markov chains using a construction technique based on a sequence of independent, identically distributed uniform random variables. This is a simple, yet powerful technique and different versions of this are used again in the construction of the Poisson process, the time homogenous Markov process, as well as the non-homogenous Markov process. Doeblin's Stationary Distribution Theorem is established and results from Ergodic Theory for these Doeblin chains are studied.

General (non-Doeblin) Markov chains are considered in Chapter 3. Stroock studies state communication and brings this together with some tools such as Doob's Stopping Time Theorem. Ergodic results are established in this context, starting with some simple results which are then refined.

Chapter 4 is a real highlight of the book. Continuous time Markov processes with values in a countable state space are studied in depth. This chapter focuses on the time-homogeneous case and starts with the construction of Poisson processes and compound Poisson processes. The Markov property is called out at each stage. These elementary stochastic processes are then used as the building blocks for the general time-homogenous Markov process (first with bounded, then unbounded transition rates). Ergodic Theory for these processes is then studied.

Chapter 5 builds towards a principle application, which is a Markov process study of simulated annealing. To get at this application, Stroock considers reversible Markov chains, reversible Markov processes, the Dirichlet form and Poincare's Inequality for this form. Gibbs states are studied next and the discussion of equilibriums leads quite naturally to both the study of simulated annealing and an extremely nice construction of a non-homogenous Markov process suited towards this study.

Chapter 6 is a primer for Lebesgue measure theory. Although this section is certainly not comprehensive, it is quite accessible, provides an interesting 'glimpse ahead' and suggests topics for further study.

Each chapter concludes with a number of really nice exercises of varying difficulty. The author is kind enough to provide some helpful hints for the more challenging problems.
Flarik
Although I like the choice of topics in this book I think many of them were made much more difficult than they should have been in large part due to cumbersome and difficult to unravel notation that obfuscates the intuitive content that needs to come through. If the author sees this comment I would greatly suggest he make attempts to ameliorate the problem for future editions.
Flarik
Although I like the choice of topics in this book I think many of them were made much more difficult than they should have been in large part due to cumbersome and difficult to unravel notation that obfuscates the intuitive content that needs to come through. If the author sees this comment I would greatly suggest he make attempts to ameliorate the problem for future editions.
Macage
I bought this book not because I needed to learn about Markov processes (I deal with them rather often) but because I wanted a text that discussed time-inhomogeneous Markov processes, however briefly. (I have been told that Doob does this, but I can't ever seem to bring myself to put in the work necessary to really appreciate his stochastic processes book.) Stroock gives a nice treatment of this topic in the context of simulated annealing, which is probably where most people would first encounter it these days.

I have not read most of the rest of the book, but it is clearly a more rigorous treatment than either Norris or Bremaud (both of which are nice for the beginner or non-mathematician), and it requires a bit more mathematical maturity. Nevertheless my sampling indicates that it is well-written. It is probably better suited for the mathematicians and probabilists (or those who will have to deal with more advanced topics later) than for the average user of Markov processes. I would recommend it, along with Williams' wonderful Probability with Martingales, to anyone who wants a really solid yet concise grounding in mathematical probability at the undergraduate level.
Macage
I bought this book not because I needed to learn about Markov processes (I deal with them rather often) but because I wanted a text that discussed time-inhomogeneous Markov processes, however briefly. (I have been told that Doob does this, but I can't ever seem to bring myself to put in the work necessary to really appreciate his stochastic processes book.) Stroock gives a nice treatment of this topic in the context of simulated annealing, which is probably where most people would first encounter it these days.

I have not read most of the rest of the book, but it is clearly a more rigorous treatment than either Norris or Bremaud (both of which are nice for the beginner or non-mathematician), and it requires a bit more mathematical maturity. Nevertheless my sampling indicates that it is well-written. It is probably better suited for the mathematicians and probabilists (or those who will have to deal with more advanced topics later) than for the average user of Markov processes. I would recommend it, along with Williams' wonderful Probability with Martingales, to anyone who wants a really solid yet concise grounding in mathematical probability at the undergraduate level.
Kefym
It's a good book introducing important concepts. Nevertheless it lacks measure theory so it is not so much for Graduates as advertised.
Kefym
It's a good book introducing important concepts. Nevertheless it lacks measure theory so it is not so much for Graduates as advertised.