Format:
Online-Ressource (X, 265 p. 27 illus., 2 illus. in color, digital)
Edition:
2nd ed. 2012
ISBN:
9781461436157
Series Statement:
Springer Texts in Statistics
Content:
Markov Chains -- Poisson Processes -- Renewal Processes -- Continuous Time Markov Chains -- Martingales -- Mathematical Finance -- A Review of Probability.
Content:
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.
Note:
Description based upon print version of record
,
Essentials of Stochastic Process; Preface; Contents; Chapter1 Markov Chains; 1.1 Definitions and Examples; 1.2 Multistep Transition Probabilities; 1.3 Classification of States; 1.4 Stationary Distributions; 1.5 Limit Behavior; 1.6 Special Examples; 1.6.1 Doubly Stochastic Chains; 1.6.2 Detailed Balance Condition; 1.6.3 Reversibility; 1.6.4 The Metropolis-Hastings Algorithm; 1.7 Proofs of the Main Theorems; 1.8 Exit Distributions; 1.9 Exit Times; 1.10 Infinite State Spaces; 1.11 Chapter Summary; 1.12 Exercises; Chapter2 Poisson Processes; 2.1 Exponential Distribution
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2.2 Defining the Poisson Process2.3 Compound Poisson Processes; 2.4 Transformations; 2.4.1 Thinning; 2.4.2 Superposition; 2.4.3 Conditioning; 2.5 Chapter Summary; 2.6 Exercises; Chapter3 Renewal Processes; 3.1 Laws of Large Numbers; 3.2 Applications to Queueing Theory; 3.2.1 GI/G/1 Queue; 3.2.2 Cost Equations; 3.2.3 M/G/1 Queue; 3.3 Age and Residual Life*; 3.3.1 Discrete Case; 3.3.2 General Case; 3.4 Chapter Summary; 3.5 Exercises; Chapter4 Continuous Time Markov Chains; 4.1 Definitions and Examples; 4.2 Computing the Transition Probability; 4.3 Limiting Behavior
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4.4 Exit Distributions and Hitting Times4.5 Markovian Queues; 4.6 Queueing Networks*; 4.7 Chapter Summary; 4.8 Exercises; Chapter5 Martingales; 5.1 Conditional Expectation; 5.2 Examples, Basic Properties; 5.3 Gambling Strategies, Stopping Times; 5.4 Applications; 5.5 Convergence; 5.6 Exercises; Chapter6 Mathematical Finance; 6.1 Two Simple Examples; 6.2 Binomial Model; 6.3 Concrete Examples; 6.4 Capital Asset Pricing Model; 6.5 American Options; 6.6 Black-Scholes Formula; 6.7 Calls and Puts; 6.8 Exercises; AppendixA Review of Probability; A.1 Probabilities, Independence
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A.2 Random Variables, DistributionsA.3 Expected Value, Moments; References; Index;
Additional Edition:
ISBN 9781461436140
Additional Edition:
Buchausg. u.d.T. Durrett, Richard, 1951 - Essentials of stochastic processes New York, NY : Springer, 2012 ISBN 9781461436140
Language:
English
Subjects:
Mathematics
Keywords:
Stochastischer Prozess
DOI:
10.1007/978-1-4614-3615-7
URL:
Volltext
(lizenzpflichtig)
Author information:
Durrett, Richard 1951-
