Elements of the Theory of Markov Processes and Their Applications

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Dover Publications, 1960 - Mathematics - 468 pages
The purpose of this excellent graduate-level text is twofold: first, to present a nonmeasure-theoretic introduction to Markov processes, and second, to give a formal treatment of mathematical models based on this theory, which have been employed in various fields. Since the main emphasis is on application, the book is intended both as a text and reference in applied probability theory. There are three parts:
Part I consists of three chapters, respectively devoted to processes discrete in space and time, processes discrete in space and continuous in time, and processes continuous in space and time (diffusion processes). Inasmuch as this section presents the elements of the theory necessary for the applications in Part II, this material can also serve as a text for an introductory course on Markov processes for students of probability and mathematical statistics, and research worked in applied fields.
Part II consists of six chapters devoted to applications in biology, physics, astronomy and astrophysics, chemistry, and operations research. An attempt has been made to consider in detail representative applications of the theory of Markov processes in the above areas, with particular emphasis on the assumptions on which the stochastic models are based and the properties of these models.
The three appendixes are concerned with generating functions, integral transforms, and Monte Carlo methods. The first two appendixes list some properties of generating functions and Laplace and Mellin transforms required in the text. The third appendix is mainly devoted to references dealing with the use of Monte Carlo methods in the study of stochastic processes occurring in different applied fields.
A bibliography is given at the end of each chapter and appendix. In addition, a general bibliography of texts and monographs on stochastic processes is given at the end of the Introduction. Prerequisites are a knowledge of elementary probability theory, mathematical statistics and analysis.

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Contents

Introduction
1
Processes Discrete in Space and Continuous in Time
57
Processes Continuous in Space and Time
129
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