Applied stochastic processes (Q2843907)

From the preface: ``The purpose of these notes is to present a concise account of applied stochastic processes [\dots]. The topics, after a quick review of basic probability, include Poisson processes, renewal processes, discrete time and continuous time Markov chains, Brownian motion, and an introduction to stochastic differential equations. [\dots] The mathematical theory is developed with strong emphasis on probability intuition, often informally, to be easy accessible, but always based on sound reasoning.''NEWLINENEWLINEThe book provides a good background for a first course on stochastic processes as it covers the main topics and contains many examples. The author gives many good explanations but he also tends to replace mathematical rigour by intuition. For example, in the case of the Poisson process, the arrival times need a definition in terms of the Poisson process and a proof of measurability, and the argument intended to prove that the inter-arrival times are independent and identically exponentially distributed is amazingly short and relies on the shift of the Poisson process by an arrival time which again is not defined. Readers of this book should be most careful with respect to the mathematical details.