### Synopses & Reviews

Applied Stochastic Processes uses a distinctly applied framework to present the most important topics in the field of stochastic processes. Key features: -Presents carefully chosen topics such as Gaussian and Markovian processes, Markov chains, Poisson processes, Brownian motion, and queueing theory -Examines in detail special diffusion processes, with implications for finance, various generalizations of Poisson processes, and renewal processes -Serves graduate students in a variety of disciplines such as applied mathematics, operations research, engineering, finance, and business administration -Contains numerous examples and approximately 350 advanced problems, reinforcing both concepts and applications -Includes entertaining mini-biographies of mathematicians, giving an enriching historical context -Covers basic results in probability Two appendices with statistical tables and solutions to the even-numbered problems are included at the end. This textbook is for graduate students in applied mathematics, operations research, and engineering. Pure mathematics students interested in the applications of probability and stochastic processes and students in business administration will also find this book useful. Bio: Mario Lefebvre received his B.Sc. and M.Sc. in mathematics from the Université de Montréal, Canada, and his Ph.D. in mathematics from the University of Cambridge, England. He is a professor in the Department of Mathematics and Industrial Engineering at the École Polytechnique de Montréal. He has written five books, including another Springer title, Applied Probability and Statistics, and has published numerous papers on applied probability, statistics, and stochastic processes in international mathematical and engineering journals. This book developed from the author's lecture notes for a course he has taught at the École Polytechnique de Montréal since 1988.

#### Review

From the reviews: "This book is an excellent reference for those interested in how probability theory can be applied to concrete problems arising in engineering, biology, management science and operation research. ... Several tables and figures enrich the book. Turning to more technical remarks, the book is certainly very well written, the proofs are clear and the examples are often illuminating. ... This book will be valuable to graduate students or professionals ... . The large number of problems makes it suitable for self study." (Fabio Mainardi, MathDL, April, 2007) "The book aims at providing the readers with a reference that covers the most important subjects in the field of stochastic processes and that is accessible to students who do not necessarily have a sound theoretical knowledge of mathematics. ... In addition to the examples presented in the theory, the book contains approximately 350 exercises, many of which are multiple-part problems." (Oleg K. Zakusilo, Zentralblatt MATH, Vol. 1127 (4), 2008) "This book on stochastic processes is aimed at mathematics students ... and students from other disciplines such as engineering. ... Each chapter is concluded with many exercises--337 in total in the book. ... In general, the book is based on the trusted principles that all functions are measurable and all distributions are either discrete, or continuous, or mixed. ... this is a well-structured text with a strong focus on doing calculations and applying the facts just learned." (Jan M. Swart, Mathematical Reviews, Issue 2008 g) "The introductory course on stochastic processes provided in this text is aimed mainly at students of (electrical) engineering and applied mathematics (operations research). ... The overall style of writing is pedagogically clear. ... Every chapter ends with numerous exercises, about 350 in total. ... Thus, the text is useful for self-study and for the intended audience of students." (Paul Embrechts, Journal of the American Statistical Association, Vol. 103 (484), December, 2008)

#### Synopsis

Applied Stochastic Processes introduces the reader to stochastic processes with a focus on the applications of the theoretical results. This text is self-contained and logically organized. It begins with a review of elementary probability, followed by an introduction to the most important subjects in the field of stochastic processes. Topics covered include Gaussian and Markovian processes, Markov Chains, Weiner and Poisson processes, Brownian motion, and queueing theory with a special highlight on diffusion processes. The reader will appreciate the clear definitions, thoroughly explained examples and interesting notes about the mathematicians referenced throughout the text. In addition, there are hundreds of advanced, multi-part problems following each chapter which enable even a novice of theoretical mathematics to master the material presented.

This textbook evolved from the author's lecture notes for a graduate-level course on applied stochastic processes. It is meant for graduate-level students in electrical engineering, applied mathematics, and notably operations research.

#### Synopsis

This book uses a distinctly applied framework to present the most important topics in stochastic processes, including Gaussian and Markovian processes, Markov Chains, Poisson processes, Brownian motion and queueing theory. The book also examines in detail special diffusion processes, with implications for finance, various generalizations of Poisson processes, and renewal processes. It contains numerous examples and approximately 350 advanced problems that reinforce both concepts and applications. Entertaining mini-biographies of mathematicians give an enriching historical context. The book includes statistical tables and solutions to the even-numbered problems at the end.

#### Synopsis

Applied Stochastic Processes presents elementary probability and stochastic processes in a clear, interesting framework that contains both practical applications and historical context. The presentation is mathematically illuminating and oriented toward science and engineering.

Self-contained and logically organized, this text includes topics such as Gaussian and Markovian processes, Markov Chains, Weiner and Poisson processes, Brownian motion and queueing theory, with a special highlight on diffusion processes. The reader will appreciate the clear definitions, thoroughly explained examples and interesting remarks about the mathematicians that are interspersed throughout the text. In addition, the concepts are reinforced by hundreds of advanced, multi-part problems following each chapter.

This textbook evolved from the author's lecture notes for a course he has taught at the cole Polytechnique de Montral since 1988. It is ideal for graduate students in operations research, electrical engineering and applied mathematics.

#### Synopsis

This book uses a distinctly applied framework to present the most important topics in stochastic processes, including Gaussian and Markovian processes, Markov Chains, Poisson processes, Brownian motion and queueing theory.

### Table of Contents

Preface.- Review of probability theory.- Stochastic processes.- Markov chains.- Diffusion processes.- Poisson processes.- Queueing theory.- Appendix A. Statistical tables.- Appendix B. Answers to even-numbered exercises.- References.- Index