Name: Essentials of Stochastic Processes By Richard Durrett
SKU: 9783319833316
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Essentials of Stochastic Processes Summary

Essentials of Stochastic Processes by Richard Durrett

Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. 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.

Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while 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 applied in the treatment of mathematical finance.

Essentials of Stochastic Processes Reviews

It is the 3rd edition of the textbook devoted to initial information and basic topics from the theory of stochastic processes. ... The book is very useful for anyone who is interested in probability theory and its ramifications and applications. It can be recommended both for students and postgraduates, teachers and practitioners. ... The book contains a lot of examples which contribute to a better understanding of the text. (Yuliya S. Mishura, zbMATH 1378.60001, 2018)

This is the third edition of a popular textbook on stochastic processes. It is intended for advanced undergraduates and beginning graduate students and aimed at an intermediate level between an undergraduate course in probability and the first graduate course that uses measure theory. (William J. Satzer, MAA Reviews, maa.org, February, 2017)

About Richard Durrett

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.

1) Markov Chains1.1 Definitions and Examples1.2 Multistep Transition Probabilities1.3 Classification of States 1.4 Stationary Distributions1.4.1 Doubly stochastic chains1.5 Detailed balance condition1.5.1 Reversibility 1.5.2 The Metropolis-Hastings algorithm1.5.3 Kolmogorow cycle condition 1.6 Limit Behavior 1.7 Returns to a fixed state 1.8 Proof of the convergence theorem*1.9 Exit Distributions 1.10 Exit Times1.11 Infinite State Spaces* 1.12 Chapter Summary1.13 Exercises
2) Poisson Processes 2.1 Exponential Distribution 2.2 Defining the Poisson Process2.2.1 Constructing the Poisson Process2.2.2 More realistic models2.3 Compound Poisson Processes 2.4 Transformations2.4.1 Thinning 2.4.2 Superposition2.4.3 Conditioning2.5 Chapter Summary2.6 Exercises
3) Renewal Processes3.1 Laws of Large Numbers3.2 Applications to Queueing Theory3.2.1 GI/G/1 queue3.2.2 Cost equations 3.2.3 M/G/1 queue3.3 Age and Residual Life*3.3.1 Discrete case3.3.2 General case 3.4 Chapter Summary 3.5 Exercises
4) Continuous Time Markov Chains 4.1 Definitions and Examples4.2 Computing the Transition Probability4.2.1 Branching Processes 4.3 Limiting Behavior 4.3.1 Detailed balance condition 4.4 Exit Distributions and Exit Times 4.5 Markovian Queues 4.5.1 Single server queues4.5.2 Multiple servers4.5.3 Departure Processes 4.6 Queueing Networks*4.7 Chapter Summary4.8 Exercises
5) Martingales 5.1 Conditional Expectation 5.2 Examples5.3 Gambling Strategies, Stopping Times 5.4 Applications 5.4.1 Exit distributions5.4.2 Exit times 5.4.3 Extinction and ruin probabilities5.4.4 Positive recurrence of the GI/G/1 queue*5.5 Exercises
6) Mathematical Finance6.1 Two Simple Examples6.2 Binomial Model 6.3 Concrete Examples 6.4 American Options6.5 Black-Scholes formula6.6 Calls and Puts6.7 Exercises
A) Review of Probability A.1 Probabilities, Independence A.2 Random Variables, Distributions A.3 Expected Value, MomentsA.4 Integration to the Limit

Additional information

Sku

NLS9783319833316

ISBN 13

9783319833316

ISBN 10

3319833316

Title

Essentials of Stochastic Processes by Richard Durrett

Author

Richard Durrett

Series

Springer Texts in Statistics

Condition

New

Binding type

Paperback

Publisher

Springer International Publishing AG

Year published

2018-04-22

Number of pages

275

Prizes

N/A

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Book picture is for illustrative purposes only, actual binding, cover or edition may vary.

Note

This is a new book - be the first to read this copy. With untouched pages and a perfect binding, your brand new copy is ready to be opened for the first time

Essentials of Stochastic Processes Richard Durrett

Essentials of Stochastic Processes by Richard Durrett

Summary

Essentials of Stochastic Processes Summary

Essentials of Stochastic Processes by Richard Durrett

Essentials of Stochastic Processes Reviews

About Richard Durrett

Table of Contents

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