Essentials of Stochastic Processes (Springer Texts in Statistics) - Hardcover

Durrett, Richard

Hardcover

ISBN 10: 038798836X ISBN 13: 9780387988368

Publisher: Springer-Verlag New York Inc., 2001

Synopsis

Stochastic processes have become important for many fields, including mathematical finance and engineering. Written by one of the worlds leading probabilists, this book presents recent results previously available only in specialized monographs. It features the introduction and use of martingales, which allow readers to do much more with Brownian motion, e.g., applications to option pricing, and integrates queueing theory into the presentation of continuous time Markov chains and renewal theory.

About this title

Review:

This book is an introduction to stochastic processes written for undergraduates or beginning grad. students who have had a previous course in probability. Durrett has sketched a 25-page review of probability at the beginning of the book, which includes many examples and some challenging exercises. The rest of the book covers discrete and continuous time Markov chains, Poisson processes, Brownian motion, and some renewal theory, including material on queuing networks, spatial Poisson processes, and a fine chapter on martingales which treats optional sampling and forms a good basis for later study of Brownian motion and applications to option pricing and the Black-Scholes formula. Durrett wants his readers to be able to use stochastic processes to solve problems. He presents numerous examples to motivate and develop skills. Examples are explained in detail, sometimes including more than one solution. After stating a result, he frequently asks "Why is this true?" and then sketches a proof or offers an intuitive answer in order to develop the reader's insight (and to allow application-oriented readers to skip the details of a formal proof). He sometimes postpones or skips rigorous proofs so he can develop and apply the theory more quickly. A reader with applications in mind, especially one already familiar with the theory, will appreciate these features. --Mathematical Reviews

About the Author:

Richard Durrett received his Ph.D. in Operations Research from Stanford in 1976. He taught at the UCLA mathematics department for 9 years and at Cornell for 25 years before moving to Duke in 2010. He is author of 8 books and more than 200 journal articles and has supervised more that 45 Ph.D. students. He is a member of the National Academy of Science. Most of his current research concerns the applications of probability to biology: ecology, genetics, and most recently cancer.

About this edition

• Publisher: Springer-Verlag New York Inc.
• Publication date: 2001
• ISBN 10: 038798836X
• ISBN 13: 9780387988368
• Binding: Hardcover
• Edition number: 2
• Number of pages: 289