Applied Probability Models with Optimization Applications

Concise advanced-level introduction to stochastic processes that arise in applied probability. Poisson process, renewal theory, Markov chains, Brownian motion, much more.

A clarity of style and a conciseness of treatment which students will find most welcome. The material is valuable and well organised… an excellent introduction to applied probability.
- Journal of the American Statistical Association. This book offers a concise introduction to some of the stochastic processes that frequently arise in applied probability. Emphasis is on optimization models and methods, particularly in the area of decision processes. After reviewing some basic notions of probability theory and stochastic processes, the author presents a useful treatment of the Poisson process, including compound and nonhomogeneous Poisson processes. Subsequent chapters deal with such topics as renewal theory and Markov chains; semi-Markov, Markov renewal, and regenerative processes; inventory theory; and Brownian motion and continuous time optimisation models. Each chapter is followed by a section of useful problems that illustrate and complement the text. There is also a short list of relevant references at the end of every chapter. Students will find this a largely self-contained text that requires little previous knowledge of the subject. It is especially suited for a one-year course in applied probability at the advanced undergraduate or beginning postgraduate level.