Modeling and analysis of stochastic systems - Kulkarni, Vidyadhar G. (Texts in statistical science, 2010)
This book is designed for two successive courses in stochastic models, with the first based on the first six chapters, and the second the last four chapters. It presents traditional material for introductory courses in stochastic processes and applied probability. (I have to confess to a small tinge of disappointment that I did not find anything startlingly unusual or innovatory in the bookbut this does not detract from its strong merits as a course text, and may even strengthen it in this regard.) It assumes knowledge of calculus and matrix algebra, but does not require measure theory. There are exercises after each chapter, generally divided into three classes: modelling, computational, and conceptual. Answers are given “to selected problems,” these being most of the odd-numbered problems. The depth is indicated by the fact that the “second course,” the more advanced last four chapters, cover queues, renewal processes, Markov regenerative processes, and diffusion processes, with the last of these including stochastic calculus, martingales, and a brief discussion of financial applications.Changes from the first edition include removal of an appendix on stochastic ordering, adding of appendices on analysis and on differential and difference equations, a new chapter on diffusion processes, deletion of discussion of numerical methods and some details of Markov renewal theory, as well as changes to the sequence of presentation of some topics. Some exercises have been deleted and new ones added.The preface ends with the mark of an enthusiast: the author says “It is my fond hope that the students will see a stochastic model lurking in every corner of their world as a result of studying this book.” That enthusiasm has translated into an accessible, well paced, and very nicely presented book. The publishers are also to be commended on its nice production: it is the sort of book which is a pleasure to read. In all, it is an excellent textbook for use in introductory courses on stochastic processes