Stochastic Processes (Classics in Applied Mathematics, Series Number 24)

This introductory textbook explains how and why probability models are applied to scientific fields such as medicine, biology, physics, oceanography, economics, and psychology to solve problems about stochastic processes. It does not just show how a problem is solved but explains why by formulating questions and first steps in the solutions. Stochastic Processes is ideal for a course aiming to give examples of the wide variety of empirical phenomena for which stochastic processes provide mathematical models. It introduces the methods of probability model building and provides the reader with mathematically sound techniques as well as the ability to further study the theory of stochastic processes. Originally published in 1962, this was the first comprehensive survey of stochastic processes requiring only a minimal background in introductory probability theory and mathematical analysis. Stochastic Processes continues to be unique, with many topics and examples still not discussed in other textbooks. As new fields of applications (such as finance and DNA analysis) become important, researchers will continue to find the fundamental and accessible topics explained in this book essential background for their research. Stochastic Processes......Page 1 Table of contents......Page 10 Preface to the Classics Edition......Page 14 Preface......Page 18 Role of the theory of stochastic processes......Page 22 CHAPTER 1 Random variables and stochastic processes......Page 28 CHAPTER 2 Conditional probability and conditional expectation......Page 62 CHAPTER 3 Normal processes and covariance stationary processes......Page 87 CHAPTER 4 Counting processes and Poisson processes......Page 138 CHAPTER 5 Renewal counting processes......Page 181 CHAPTER 6 Markov chains:discrete parameter......Page 208 CHAPTER 7 Markov chains:continuous parameter......Page 297 References......Page 328 Author index......Page 335 Subject index......Page 337 The math which goes into stochastic theory is key and fundamental; this book is a very readable introduction to the material. Where most books just have the equations (and typically in the tersest form possible), this book makes an effort to explain what is going on "in words" and through some examples. If you are in a class or working with material where a firm understanding of stochastic theory is necessary, this is a good book to help you get up to speed. This is definitely not an advanced-level book or completely up-to-date, but the basics haven't changed. If you can find it used, it is cheap, too.