×

zbMATH — the first resource for mathematics

Modeling and analysis of stochastic systems. (English) Zbl 0866.60004
London: Chapman & Hall. xi, 619 p. (1995).
This is a beautiful introductory textbook on stochastic processes covering following issues: discrete and continuous time Markov chains (and Poisson process as a separate item), renewal and regeneration processes, and Markov renewal processes (just in this order, that causes several forward references; the author stresses that consideration of Markov chains before renewal theory enables students to build numerous stochastic models at the very beginning of the course). The development of each class of processes follows a common pattern: transition distribution, stationary behaviour, cost/reward analysis, first passage times. Complicated questions (such as the proof of the key renewal theorem, general state space considerations, etc.) are omitted, so the reader needs only basic knowledge in calculus, probability and matrix algebra. Plenty of applications, examples and exercises brings the reader to the intuitive understanding of the subject.

MSC:
60-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory
60Jxx Markov processes
60Kxx Special processes
PDF BibTeX Cite