A First Course in Stochastic Processes

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Academic Press, Dec 2, 2012 - Mathematics - 557 pages
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The purpose, level, and style of this new edition conform to the tenets set forth in the original preface. The authors continue with their tack of developing simultaneously theory and applications, intertwined so that they refurbish and elucidate each other.
The authors have made three main kinds of changes. First, they have enlarged on the topics treated in the first edition. Second, they have added many exercises and problems at the end of each chapter. Third, and most important, they have supplied, in new chapters, broad introductory discussions of several classes of stochastic processes not dealt with in the first edition, notably martingales, renewal and fluctuation phenomena associated with random sums, stationary stochastic processes, and diffusion theory.
 

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Contents

Chapter 1 ELEMENTS OF STOCHASTIC PROCESSES
1
Chapter 2 MARKOV CHAINS
45
Chapter 3 THE BASIC LIMIT THEOREM OF MARKOV CHAINS AND APPLICATIONS
81
Chapter 4 CLASSICAL EXAMPLES OF CONTINUOUS TIME MARKOV CHAINS
117
Chapter 5 RENEWAL PROCESSES
167
Chapter 6 MARTINGALES
238
Chapter 7 BROWNIAN MOTION
340
Chapter 8 BRANCHING PROCESSES
392
Chapter 9 STATIONARY PROCESSES
443
REVIEW OF MATRIX ANALYSIS
536
Index
553
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About the author (2012)

Howard E. Taylor is a research chemist with the National Research Program, Water Resources Division, U.S. Geological Survey located in Boulder, Colorado. Dr. Taylor has played a major role over the past 25 years in the development of plasma spectrometric techniques in analytical chemistry, as reflected in his more than 150 technical publications and the presentation of numerous papers at national and international technical meetings. He has served as faculty affiliate at Colorado State University and has taught American Chemical Society Short Courses for more than 15 years.

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