Introduction to Markov Chains
With Special Emphasis on Rapid Mixing
(Sprache: Englisch)
The aims of this book are threefold:
We start with a naive description of a Markov chain as a memoryless random walk on a finite set. This is complemented by a rigorous definition in the framework of probability theory, and then we develop the most...
We start with a naive description of a Markov chain as a memoryless random walk on a finite set. This is complemented by a rigorous definition in the framework of probability theory, and then we develop the most...
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Klappentext zu „Introduction to Markov Chains “
The aims of this book are threefold:We start with a naive description of a Markov chain as a memoryless random walk on a finite set. This is complemented by a rigorous definition in the framework of probability theory, and then we develop the most important results from the theory of homogeneous Markov chains on finite state spaces.
Chains are called rapidly mixing if all of the associated walks, regardles of where they started, behave similarly already after comparitively few steps: it is impossible from observing the chain to get information on the starting position or the number of steps done so far. We will thoroughly study methods which have been proposed in the last decades to investigate this phenomenon.
A number of examples will be studied to indicate how the methods treated in this book can be applied.
Inhaltsverzeichnis zu „Introduction to Markov Chains “
Besides the investigation of general chains the book contains chapters which are concerned with eigenvalue techniques, conductance, stopping times, the strong Markov property, couplings, strong uniform times, Markov chains on arbitrary finite groups (including a crash-course in harmonic analysis), random generation and counting, Markov random fields, Gibbs fields, the Metropolis sampler, and simulated annealing. With 170 exercises.Autoren-Porträt von Ehrhard Behrends
Prof. Dr. Ehrhard Behrends ist am Fachbereich Mathematik der Freien Universität Berlin tätig.
Bibliographische Angaben
- Autor: Ehrhard Behrends
- 1999, 2000, 234 Seiten, Maße: 18,4 x 25,8 cm, Kartoniert (TB), Englisch
- Verlag: Vieweg+Teubner
- ISBN-10: 3528069864
- ISBN-13: 9783528069865
Sprache:
Englisch
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