Continuous-Time Markov Chains: An Applications-Oriented Approach

✍ Scribed by William J. Anderson (auth.)

• Publisher: Springer-Verlag New York
• Year: 1991
• Tongue: English
• Leaves: 366
• Series: Springer Series in Statistics
• Edition: 1
• Category: Library

✦ Synopsis

Continuous time parameter Markov chains have been useful for modeling various random phenomena occurring in queueing theory, genetics, demography, epidemiology, and competing populations. This is the first book about those aspects of the theory of continuous time Markov chains which are useful in applications to such areas. It studies continuous time Markov chains through the transition function and corresponding q-matrix, rather than sample paths. An extensive discussion of birth and death processes, including the Stieltjes moment problem, and the Karlin-McGregor method of solution of the birth and death processes and multidimensional population processes is included, and there is an extensive bibliography. Virtually all of this material is appearing in book form for the first time.

✦ Table of Contents

Front Matter....Pages i-xii
Transition Functions and Resolvents....Pages 1-60
Existence and Uniqueness of Q -Functions....Pages 61-91
Examples of Continuous-Time Markov Chains....Pages 92-119
More on the Uniqueness Problem....Pages 120-154
Classification of States and Invariant Measures....Pages 155-203
Strong and Exponential Ergodicity....Pages 204-232
Reversibility, Monotonicity, and Other Properties....Pages 233-260
Birth and Death Processes....Pages 261-291
Population Processes....Pages 292-332
Back Matter....Pages 333-355

✦ Subjects

Probability Theory and Stochastic Processes