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A First Course in Stochastic Processes, Second Edition, by Samuel Karlin, Howard M. Taylor
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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.
- Sales Rank: #744809 in Books
- Published on: 1975-04-11
- Original language: English
- Number of items: 1
- Dimensions: 9.32" h x 1.25" w x 6.34" l, 2.05 pounds
- Binding: Hardcover
- 557 pages
About the Author
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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A challenging but enjoyable experience: Read a bit of Feller first.
By Effortful
I am quite enjoying this book. The mathematics is meticulous. As the motivation for some material has not always been clear, I have found it helpful to study this text along side two others: One is Feller - "An Introduction to Probability Theory and its Applications, volume 1." Feller is great in providing deep insight into how the mathematics arises from the nature of the problem and its formulation. Additionally, Feller provides innumerable examples that help. Pay special attention to chapters 11 and 13 of Feller - those on generating functions and recurrent events and renewal theory, respectively. Feller's intuitive derivation of many of the equations are very helpful. Feller also provides a nice chapter (15) on Markov chains.
Another useful text, I have found, is Karlin's later text, "An Introduction to Stochastic Modeling." This text is more elementary. However, it often provides insight and explanations to material that "A First Course" omits.
The analysis mathematics background required for "A First Course in Stochastic Processes" is equivalent to the analysis one gets from 'baby' Rudin, chapters 1 - 7, say. Those are enough I think. A decent probability course is useful, of course.
Read chapters 11 and 13 from Feller first. Then jump into Karlin. It's a challenging but an enjoyable experience.
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