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Denumerable Markov Chains = Generati...

Woess, Wolfgang,

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Denumerable Markov Chains = Generating Functions, Boundary Theory, Random Walks on Trees /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Denumerable Markov Chains/ Wolfgang Woess
Reminder of title:	Generating Functions, Boundary Theory, Random Walks on Trees /
Author:	Woess, Wolfgang,
Published:	Zuerich, Switzerland :European Mathematical Society Publishing House, : 2009,
Description:	1 online resource (368 pages)
Subject:	Probability & statistics -
Online resource:	https://doi.org/10.4171/071
Online resource:	https://www.ems-ph.org/img/books/woess_mini.jpg
ISBN:	9783037195710

Denumerable Markov Chains = Generating Functions, Boundary Theory, Random Walks on Trees /
Woess, Wolfgang,

Denumerable Markov ChainsGenerating Functions, Boundary Theory, Random Walks on Trees /[electronic resource] :Wolfgang Woess - Zuerich, Switzerland :European Mathematical Society Publishing House,2009 - 1 online resource (368 pages) - EMS Textbooks in Mathematics (ETB).

Restricted to subscribers:https://www.ems-ph.org/ebooks.php

Markov chains are the first and most important examples of random processes. This book is about time-homogeneous Markov chains that evolve with discrete time steps on a countable state space. Measure theory is not avoided, careful and complete proofs are provided. A specific feature is the systematic use, on a relatively elementary level, of generating functions associated with transition probabilities for analyzing Markov chains. Basic definitions and facts include the construction of the trajectory space and are followed by ample material concerning recurrence and transience, the convergence and ergodic theorems for positive recurrent chains. There is a side-trip to the Perron-Frobenius theorem. Special attention is given to reversible Markov chains and to basic mathematical models of "population evolution" such as birth-and-death chains, Galton-Watson process and branching Markov chains. A good part of the second half is devoted to the introduction of the basic language and elements of the potential theory of transient Markov chains. Here the construction and properties of the Martin boundary for describing positive harmonic functions are crucial. In the long final chapter on nearest neighbour random walks on (typically infinite) trees the reader can harvest from the seed of methods laid out so far, in order to obtain a rather detailed understanding of a specific, broad class of Markov chains. The level varies from basic to more advanced, addressing an audience from master's degree students to researchers in mathematics, and persons who want to teach the subject on a medium or advanced level. A specific characteristic of the book is the rich source of classroom-tested exercises with solutions.

ISBN: 9783037195710

Standard No.: 10.4171/071doiSubjects--Topical Terms:

3480817
Probability & statistics

Denumerable Markov Chains = Generating Functions, Boundary Theory, Random Walks on Trees /
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520 $a Markov chains are the first and most important examples of random processes. This book is about time-homogeneous Markov chains that evolve with discrete time steps on a countable state space. Measure theory is not avoided, careful and complete proofs are provided. A specific feature is the systematic use, on a relatively elementary level, of generating functions associated with transition probabilities for analyzing Markov chains. Basic definitions and facts include the construction of the trajectory space and are followed by ample material concerning recurrence and transience, the convergence and ergodic theorems for positive recurrent chains. There is a side-trip to the Perron-Frobenius theorem. Special attention is given to reversible Markov chains and to basic mathematical models of "population evolution" such as birth-and-death chains, Galton-Watson process and branching Markov chains. A good part of the second half is devoted to the introduction of the basic language and elements of the potential theory of transient Markov chains. Here the construction and properties of the Martin boundary for describing positive harmonic functions are crucial. In the long final chapter on nearest neighbour random walks on (typically infinite) trees the reader can harvest from the seed of methods laid out so far, in order to obtain a rather detailed understanding of a specific, broad class of Markov chains. The level varies from basic to more advanced, addressing an audience from master's degree students to researchers in mathematics, and persons who want to teach the subject on a medium or advanced level. A specific characteristic of the book is the rich source of classroom-tested exercises with solutions.
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