Wow! eBook
Denumerable Markov Chains: Generating Functions, Boundary Theory, Random Walks on Trees
Author(s): Wolfgang Woess (Author)
- Publisher: European Mathematical Society
- Publication Date: 15 Aug. 2009
- Language: English
- Print length: 368 pages
- ISBN-10: 303719071X
- ISBN-13: 9783037190715
Book Description
Markov chains are among the basic 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. 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 constru
