### 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.

#### 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