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Statistics - Statistical Theory and Methods | Essentials of Stochastic Processes

Essentials of Stochastic Processes

Durrett, Richard

2nd ed. 2012, X, 266 p.

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  • More than 300 exercises for effective learning
  • Includes problems with solutions and new examples
  • Significant revision to the successful first edition

This book is for a first course in stochastic processes taken by undergraduates or master’s students who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and mathematical finance. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding

 

The book has undergone a thorough revision since the first edition. There are many new examples and problems with solutions that use the TI-83 to eliminate the tedious details of solving linear equations by hand. Some material that was too advanced for the level has been eliminated while the treatment of other topics useful for applications has been expanded.  In addition, the ordering of topics has been improved. For example, the difficult subject of martingales is delayed until its usefulness can be seen in the treatment of mathematical finance.

 

Richard Durrett received his Ph.D. in Operations Research from Stanford in 1976. He taught at the UCLA math department for nine years and at Cornell for twenty-five before moving to Duke in 2010. He is the author of 8 books and almost 200 journal articles, and has supervised more that 40 Ph.D. students. Most of his current research concerns the applications of probability to biology: ecology, genetics, and most recently cancer.

Content Level » Graduate

Keywords » Markov Chains - Martingales - Mathematical Finance - Stochastic Processes

Related subjects » Applications - Probability Theory and Stochastic Processes - Statistical Theory and Methods

Table of contents 

1. Markov Chains; 2. Martingales; 3. Poisson Processes; 4. Markov Chains; 5. Renewal Theory; 6. Brownian Motion

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