Basics of applied stochastic processes / Richard Serfozo

This text book by Richard Serfozo is an introduction to the field of stochastic processes and their applications. It provides an overview of theory and applications for five classical classes of stochastic processes: Markov chains in discrete and continuous time, renewal processes, Poisson processes and Brownian motion. For each class construction and basic properties are discussed. Besides the special properties of each process many general techniques such as coupling for Markov processes, Palm theory or different convergence concepts are introduced. Of course also generalizations or important subclasses as for example Cox processes or Brownian motion in a random environment are treated in the sequel. Thereby, the text aims to be mathematically rigorous while still providing an intuitive feel for underlying principles.

The second main theme of the book is stochastic modeling. The use of stochastic processes in many fields of application is illustrated by examples from stochastic networks, queuing systems, reversible processes or population dynamics.

The text is complemented by a large number of exercises. The clear writing style and the few mathematical prerequisites (mainly elementary real analysis and basic probability theory) make it suitable for a first course in stochastic processes. But also for researchers in various fields of applications the volume is a valuable reference. (Zentralblatt)