An introduction to stochastic modeling. Revised ed.

*(English)*Zbl 0796.60001
Boston, MA: Academic Press, Inc.. xi, 566 p. (1994).

This textbook is intended to introduce on the basis of a course on elementary probability calculus (no measure theory or general integral calculus is needed) the concepts of fundamental stochastic processes in the modeling of real world phenomena. The contents are (compared to the first edition) mainly unchanged – with one exception: the number of exercises is nearly doubled. The topics covered and these exercises make this book a valuable addendum to any course on stochastic modeling and stochastic processes – even on a much more advanced level: Markov chains in discrete time; Poisson processes; Continuous time Markov chains; Renewal processes; Branching processes; Queueing systems.

The book is clearly written, the presentation and style nearly ideal for the expected readership (students in the fields of mathematics and its applications, as well as students in Operations Research, Electrical and Industrial Engineering, etc.). Important techniques (e.g., first step analysis, renewal arguments) are presented with many details, examples and explicit computations. It is worth to notice that even on the elementary level the authors introduce non-standard models and processes to the beginner, which lead even into the neighbourhood of recent research, e.g.: Spatial Poisson processes; Compound and marked Poisson processes; Set valued Markov processes; Queueing networks.

The book will not only inspire the readers for the field of stochastic processes, but it indicates undoubtedly the limitations given by the still elementary mathematics. That is, it will become clear from the applications the necessity of having stronger techniques at hand when dealing with more complex real world phenomena.

The book is clearly written, the presentation and style nearly ideal for the expected readership (students in the fields of mathematics and its applications, as well as students in Operations Research, Electrical and Industrial Engineering, etc.). Important techniques (e.g., first step analysis, renewal arguments) are presented with many details, examples and explicit computations. It is worth to notice that even on the elementary level the authors introduce non-standard models and processes to the beginner, which lead even into the neighbourhood of recent research, e.g.: Spatial Poisson processes; Compound and marked Poisson processes; Set valued Markov processes; Queueing networks.

The book will not only inspire the readers for the field of stochastic processes, but it indicates undoubtedly the limitations given by the still elementary mathematics. That is, it will become clear from the applications the necessity of having stronger techniques at hand when dealing with more complex real world phenomena.

Reviewer: H.Daduna (Hamburg)

##### MSC:

60-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory |

60Jxx | Markov processes |

60Kxx | Special processes |