Stochastic Processes - Hardcover

Medhi, J.

Hardcover

ISBN 10: 0470220538 ISBN 13: 9780470220535

Publisher: Wiley, 1994

Synopsis

Revised and updated to provide a better, broader and more elaborate exposure of the subject. New to this edition: numerous application examples and exercises of stochastic processes in engineering systems and management; detailed and current material on Markov chains, Martingales, renewal theory, queueing and reliability; more information on the latest research including the regenerative (stochastic) inventory system; an up-to-date extensive bibliography and references at each chapter's end.

About this title

About the Author

Jyotiprasad Medhi, Professor Emeritus, was a visiting professor at the Universities of Montreal, McMaster and Toronto (Canada), and University of Wisconsin (USA).

He is the author/co-author of a large number of scientific/technical papers published in international journals and has been working as referee to many reputed international journals. He has also been giving seminar lectures at several Universities in India, UK, France, Canada and U.S.A.

In addition to publishing a large number of research papers and an introductory text Statistical Methods, he has authored three advanced level books Stochastic Processes, Recent Developments in Bulk Queueing Models and Stochastic Models in Queueing Theory, published in India and USA.

Review

A review of the first edition in The American Mathematical Monthly (Dec., 1982) gives a special positive emphasis on it as a textbook as this is the clear choice amongst a dozen or more competing texts. (TAV) Similarly a review of the second edition (1994) in the Journal of the Operational Research Society, U.K. (1996) commended it As before, it rightly deserves to be 'nominated' as the first choice. (Jim Freeman)

A review of the first edition in The American Mathematical Monthly (Dec., 1982) gives a special positive emphasis on it as a textbook as 'this is the clear choice amongst a dozen or more competing texts'. --TAV

Similarly a review of the second edition (1994) in the Journal of the Operational Research Society, U.K. (1996) commended it 'As before, it rightly deserves to be 'nominated' as the first choice'. --Jim Freeman

Similarly a review of the second edition (1994) in the Journal of the Operational Research Society, U.K. (1996) commended it 'As before, it rightly deserves to be 'nominated' as the first choice'. --Jim Freeman

Medhi has written a Stochastic Processes book in the classic style, just the way I like it. The chapter titles are: 1. Random Variables and Stochastic Processes, 2. Markov Chains, 3. Markov Processes With Discrete State Space: Poisson Process and Its Extensions, 4. Markov Processes With Continuous State Space, 5. Martingales, 6. Renewal Processes and Theory, 7. Markov Renewal and Semi-Markov Processes, 8. Stationary Processes and Time Series, 9. Branching Processes, 10. Applications in Stochastic Models, 11. Simulation.

Chapter 4 is mainly about Brownian motion and Chapter 10 is mainly about queueing theory. [Medhi is the author of an excellent queueing theory text as well (Medhi 2003).] Chapter 2 includes a graph-theoretic approach to Markov chains and statistical inference for Markov chains, topics not found in most other stochastic processes books. Appendix A covers some mathematical background including results on Laplace transforms, difference equations, and matrices. It is appropriate to compare the third edition to the second edition (1994). In addition to some changes in presentation, there are new chapters on martingales and simulation. The third edition also has an improved printing style and binding. In addition, the table of contents has been greatly expanded to include subsections. This is of great value in searching for a particular topic. The index has expanded as well. Although the bulk of material in the third edition is similar to the second edition, the third edition is a considerable improvement over the earlier work.

I especially like the writing style of Medhi, which is reader friendly. He goes out of his way to add clarity if a topic has potential confusion. He addresses a reader's questions even before the reader has managed to formulate those questions. It is instructive to see a master expositor in action. The exercises vary in difficulty, and include standard calculations, questions aimed to improve the understanding of the material, and other interesting topics that were not part of the general presentation in the expository sections. Some of the exercises have answers, some have partial solutions, others have neither (the latter are usually questions which ask the reader to show some relationship holds). I especially like the topics of the exercises as they make the reader think in new ways and wonder over extensions and possible modifications of the problems.

An author has to choose what to include and exclude in the choice of topics, examples, and exercises. Medhi's choice of topics is most appropriate for a stochastic processes book. The choice of examples used to illustrate the general concepts is excellent, helped by the author's years of experience. Medhi also includes bits of history in his presentation, and has excellent bi --Myron Hlynka, University of Windsor, TECHNOMETRICS, MAY 2011, VOL. 53, NO. 2 221-222 ( BOOK REVIEWS SECTION)

Medhi has written a Stochastic Processes book in the classic style, just the way I like it. The chapter titles are: 1. Random Variables and Stochastic Processes, 2. Markov Chains, 3. Markov Processes With Discrete State Space: Poisson Process and Its Extensions, 4. Markov Processes With Continuous State Space, 5. Martingales, 6. Renewal Processes and Theory, 7. Markov Renewal and Semi-Markov Processes, 8. Stationary Processes and Time Series, 9. Branching Processes, 10. Applications in Stochastic Models, 11. Simulation.

Chapter 4 is mainly about Brownian motion and Chapter 10 is mainly about queueing theory. [Medhi is the author of an excellent queueing theory text as well (Medhi 2003).] Chapter 2 includes a graph-theoretic approach to Markov chains and statistical inference for Markov chains, topics not found in most other stochastic processes books. Appendix A covers some mathematical background including results on Laplace transforms, difference equations, and matrices. It is appropriate to compare the third edition to the second edition (1994). In addition to some changes in presentation, there are new chapters on martingales and simulation. The third edition also has an improved printing style and binding. In addition, the table of contents has been greatly expanded to include subsections. This is of great value in searching for a particular topic. The index has expanded as well. Although the bulk of material in the third edition is similar to the second edition, the third edition is a considerable improvement over the earlier work.

I especially like the writing style of Medhi, which is reader friendly. He goes out of his way to add clarity if a topic has potential confusion. He addresses a reader's questions even before the reader has managed to formulate those questions. It is instructive to see a master expositor in action. The exercises vary in difficulty, and include standard calculations, questions aimed to improve the understanding of the material, and other interesting topics that were not part of the general presentation in the expository sections. Some of the exercises have answers, some have partial solutions, others have neither (the latter are usually questions which ask the reader to show some relationship holds). I especially like the topics of the exercises as they make the reader think in new ways and wonder over extensions and possible modifications of the problems.

An author has to choose what to include and exclude in the choice of topics, examples, and exercises. Medhi's choice of topics is most appropriate for a stochastic processes book. The choice of examples used to illustrate the general concepts is excellent, helped by the author's years of experience. Medhi also includes bits of history in his presentation, and has excellent bibliographic references and brief discussions. All of this adds to the overall material and keeps the reader interested in moving forward. In presenting material to students, I often look through several books hoping for a particular style and order of presentation, and a natural set of examples. More often than not, Medhi's choices are far closer to what I want than the presentations of other books.

The book is a masterpiece by a distinguished expert in the field. It should be in the library of every university and every student and researcher in probability, and it should be used as a text in classrooms around the world. My copy sits on my desk so that I can have ready access to it at all times. --Myron Hlynka, University of Windsor, TECHNOMETRICS, MAY 2011, VOL. 53, NO. 2 221-222 ( BOOK REVIEWS SECTION)

Edition details

• Publisher: Wiley
• Publication date: 1994
• ISBN 10: 0470220538
• ISBN 13: 9780470220535
• Binding: Hardcover
• Language: English
• Edition number: 2
• Number of pages: 598