CLASSICAL AND SPATIAL STOCHASTIC PROCESSES

This book is intended as a text for a first course in stochastic processes at the upper undergraduate or graduate levels, assuming only that the reader has had a serious calculus course-advanced calculus would even be better-as well as a first course in probability (without measure theory). In guiding the student from the simplest classical models to some of the spatial models, currently the object of considerable research, the text is aimed at a broad audience of students in biology, engineering, mathematics, and physics. The first two chapters deal with discrete Markov chains-recurrence and tran- sience, random walks, birth and death chains, ruin problem and branching pro- cesses-and their stationary distributions. These classical topics are treated with a modem twist: in particular, the coupling technique is introduced in the first chap- ter and is used throughout. The third chapter deals with continuous time Markov chains-Poisson process, queues, birth and death chains, stationary distributions.