“This text maintains the highest possible mathematical standards for a book at this level. I would not teach a course in stochastic processes without it.” — John Angus, Claremont Graduate University
“Concise and very good for a one-semester course.” — Ebenezer George, University of Memphis
“I consider this text to be the best of its kind.” — O. Enchev, Boston University
“This book is well structured with topics that can be covered in one semester. I particularly like the topics chosen because they are not only of importance in theory, but also applicable to many areas such as economics, finance, engineering, and so on. The presentation is clear and reader friendly.” — Yimin Xiao, Michigan State University
“A classic book that looks better and better as time goes by.” — N. D. Singpurwalla, George Washington University
203 pages, $54.95 list
0-88133-267-4
978-0-88133-267-4
© 1972
paperback
eBook availability
Introduction to Stochastic Processes
An excellent introduction for computer scientists and electrical and electronics engineers who would like to have a good, basic understanding of stochastic processes! This clearly written book responds to the increasing interest in the study of systems that vary in time in a random manner. It presents an introductory account of some of the important topics in the theory of the mathematical models of such systems. The selected topics are conceptually interesting and have fruitful application in various branches of science and technology.
Reactions
1. Markov Chains
Markov chains having two states / Transition function and initial distribution / Examples / Computations with transition functions / Transient and recurrent states / Decomposition of the state space / Birth and death chains / Branching and queuing chains / Proof of results for the branching and queuing chains
2. Stationary Distributions of a Markov Chain
Elementary properties of stationary distributions / Examples / Average number of visits to a recurrent state / Null recurrent and positive recurrent states / Existence and uniqueness of stationary disruptions / Queuing chain / Convergence to the stationary disruption / Proof of convergence
3. Markov Pure Jump Processes
Construction of jump processes / Birth and death processes / Properties of a Markov pure jump process
4. Second Order Processes
Mean and covariance functions / Gaussian processes / The Wiener process
5. Continuity, Integration, and Differentiation of Second Order Processes
Continuity assumptions / Integration / Differentiation / White noise
6. Stochastic Differential Equations, Estimation Theory, and Spectral Distributions
First order differential equations / Differential equations of order n / Estimation theory / Spectral distribution
Markov chains having two states / Transition function and initial distribution / Examples / Computations with transition functions / Transient and recurrent states / Decomposition of the state space / Birth and death chains / Branching and queuing chains / Proof of results for the branching and queuing chains
2. Stationary Distributions of a Markov Chain
Elementary properties of stationary distributions / Examples / Average number of visits to a recurrent state / Null recurrent and positive recurrent states / Existence and uniqueness of stationary disruptions / Queuing chain / Convergence to the stationary disruption / Proof of convergence
3. Markov Pure Jump Processes
Construction of jump processes / Birth and death processes / Properties of a Markov pure jump process
4. Second Order Processes
Mean and covariance functions / Gaussian processes / The Wiener process
5. Continuity, Integration, and Differentiation of Second Order Processes
Continuity assumptions / Integration / Differentiation / White noise
6. Stochastic Differential Equations, Estimation Theory, and Spectral Distributions
First order differential equations / Differential equations of order n / Estimation theory / Spectral distribution