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Synopsis
Continuous time parameter Markov chains have been useful for modelling various random phenomena occurring in queueing theory, genetics, demography, epidemiology, and competing populations. This book is 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. A 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 multi-dimensional population processes is included, and there is a detailed bibliography. Virtually all of this material is appearing in book form for the first time. This monograph on probability and statistics, medical statistics, documentation, biomathematics, and genetics is intended for applied probabilists, researchers in queueing theory, genetics, demography, epidemiology, and competing populations.
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