Essentials of Stochastic Processes

Name: Essentials of Stochastic Processes
Author: Richard Durrett

Paperback Engels 2018 3e druk 9783319833316

78,99

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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.

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ISBN13:9783319833316

Taal:Engels

Bindwijze:paperback

Uitgever:Springer International Publishing

Druk:3

Serie:Springer Texts in Statistics

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Inhoudsopgave

<div>1) Markov Chains</div><div>1.1 Definitions and Examples</div><div>1.2 Multistep Transition Probabilities</div><div>1.3 Classification of States </div><div>1.4 Stationary Distributions</div><div>1.4.1 Doubly stochastic chains</div><div>1.5 Detailed balance condition</div><div>1.5.1 Reversibility </div><div>1.5.2 The Metropolis-Hastings algorithm</div><div>1.5.3 Kolmogorow cycle condition </div><div>1.6 Limit Behavior </div><div>1.7 Returns to a fixed state </div><div>1.8 Proof of the convergence theorem*</div><div>1.9 Exit Distributions </div><div>1.10 Exit Times</div><div>1.11 Infinite State Spaces* </div><div>1.12 Chapter Summary</div><div>1.13 Exercises</div><div><br></div><div>2) Poisson Processes </div><div>2.1 Exponential Distribution </div><div>2.2 Defining the Poisson Process</div><div>2.2.1 Constructing the Poisson Process</div><div>2.2.2 More realistic models</div><div>2.3 Compound Poisson Processes </div><div>2.4 Transformations</div><div>2.4.1 Thinning </div><div>2.4.2 Superposition</div><div>2.4.3 Conditioning</div><div>2.5 Chapter Summary</div><div>2.6 Exercises </div><div><br></div><div>3) Renewal Processes</div><div>3.1 Laws of Large Numbers</div><div>3.2 Applications to Queueing Theory</div><div>3.2.1 GI/G/1 queue</div><div>3.2.2 Cost equations </div><div>3.2.3 M/G/1 queue</div><div>3.3 Age and Residual Life*</div><div>3.3.1 Discrete case</div><div>3.3.2 General case </div><div>3.4 Chapter Summary </div><div>3.5 Exercises</div><div><br></div><div>4) Continuous Time Markov Chains </div><div>4.1 Definitions and Examples</div><div>4.2 Computing the Transition Probability</div><div>4.2.1 Branching Processes </div><div>4.3 Limiting Behavior </div><div>4.3.1 Detailed balance condition </div><div>4.4 Exit Distributions and Exit Times </div><div>4.5 Markovian Queues </div><div>4.5.1 Single server queues</div><div>4.5.2 Multiple servers</div><div>4.5.3 Departure Processes </div><div>4.6 Queueing Networks*</div><div>4.7 Chapter Summary</div><div>4.8 Exercises </div><div><br></div><div>5) Martingales </div><div>5.1 Conditional Expectation </div><div>5.2 Examples</div><div>5.3 Gambling Strategies, Stopping Times </div><div>5.4 Applications </div><div>5.4.1 Exit distributions</div><div>5.4.2 Exit times </div><div>5.4.3 Extinction and ruin probabilities</div><div>5.4.4 Positive recurrence of the GI/G/1 queue*</div><div>5.5 Exercises</div><div><br></div><div>6) Mathematical Finance</div><div>6.1 Two Simple Examples</div><div>6.2 Binomial Model </div><div>6.3 Concrete Examples </div><div>6.4 American Options</div><div>6.5 Black-Scholes formula</div><div>6.6 Calls and Puts</div><div>6.7 Exercises</div><div><br></div><div>A) Review of Probability </div><div>A.1 Probabilities, Independence </div><div>A.2 Random Variables, Distributions </div><div>A.3 Expected Value, Moments</div>A.4 Integration to the Limit <div><br></div>

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