Passage Times for Markov Chains, Vol. 1 Book

This book is a survey of work on passage times in stable Markov chains with a discrete state space and a continuous time. Passage times have been investigated since early days of probability theory and its applications. The best known example is the first entrance time to a set, which embraces waiting times, busy periods, absorption problems, extinction phenomena, etc. Another example of great interest is the last exit time from a set. The book presents a unifying treatment of passage times, written in a systematic manner and based on modern developments. The appropriate unifying framework is provided by probabilistic potential theory, and the results presented in the text are interpreted from this point of view. In particular, the crucial role of the Dirichlet problem and the Poisson equation is stressed. The work is addressed to applied probalilists, and to those who are interested in applications of probabilistic methods in their own areas of interest. The level of presentation is that of a graduate text in applied stochastic processes. Hence, clarity of presentation takes precedence over secondary mathematical details whenever no serious harm may be expected. Advanced concepts described in the text gain nowadays growing acceptance in applied fields, and it is hoped that this work will serve as an useful introduction.

Abstracted by Mathematical Reviews, issue 94c

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The main theme of this book is that the appropriate unifying framework for discussion of passage times is provided by the probabilistic potential theory. Results of both theoretical and practical importance are discussed. Concepts of potentials, excessive functions and measures, balayage and duality are used. The crucial role of the Dirichlet problem and the Poisson equation, and various decomposition theorems is stressed. The four chapters cover analytic and measure theory, and applications. Annotation c. Book News, Inc., Portland, OR (booknews.com)