Chapman and Hall/CRC
Applied Stochastic Processes presents a concise, graduate-level treatment of the subject, emphasizing applications and practical computation. It also establishes the complete mathematical theory in an accessible way.
After reviewing basic probability, the text covers Poisson processes, renewal processes, discrete- and continuous-time Markov chains, and Brownian motion. It also offers an introduction to stochastic differential equations. While the main applications described are queues, the book also considers other examples, such as the mathematical model of a single stock market.
With exercises in most sections, this book provides a clear, practical introduction for beginning graduate students. The material is presented in a straightforward manner using short, motivating examples. In addition, the author develops the mathematical theory with a strong emphasis on probability intuition.
Probability and Stochastic Processes. Poisson Processes. Renewal Processes. Discrete-Time Markov Chains. Continuous-Time Markov Chains. Brownian Motion and Beyond. Bibliography. Index.