Essentials of Stochastic Processes / Edition 2

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This book is for a first course on stochastic processes to be taken by undergraduates or masters students who have had a course in probability theory, but who have not had a course in measure theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal theory, and Brownian motion and martingales. The last two topics are important for the brief treatment of option pricing.. "The book presents only the essentials of the subject, the parts of the theory most important for applications. To allow readers to choose their own level of detail, many of the proofs begin with a nonrigorous answer to the question "Why is this true?" followed by a proof that fills in the missing details.
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Editorial Reviews

From the Publisher
From the reviews of the second edition:

“The book consists of six chapters and 265 pages. … Each chapter has a chapter summary before the exercises. The chapter summary restates the theorems of each section and adds short new commentary. … With its many examples and applications, chosen from the broad experience of the author, this book is an excellent text for a course in applied probability.” (Myron Hlynka, Mathematical Reviews, February, 2014)

“This is the second edition of introductory text book on shastic processes by Richard Durrett. … The new edition contains many new examples and problems. The chapters have been reorganized to facilitate the learning process. … The new edition makes the topic of shastic processes even more accessible for undergraduate students and people coming from fields of applications.” (H. M. Mai, Zentralblatt MATH, Vol. 1244, 2012)

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Product Details

  • ISBN-13: 9781461436140
  • Publisher: Springer New York
  • Publication date: 5/23/2012
  • Series: Springer Texts in Statistics Series
  • Edition description: 2nd ed. 2012
  • Edition number: 2
  • Pages: 266
  • Sales rank: 416,336
  • Product dimensions: 6.20 (w) x 9.20 (h) x 0.80 (d)

Meet the Author

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.

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Table of Contents

Review of Probability
--Probabilities, Independence
--Random Variables, Distributions
--Expected Value, Moments

1   Markov Chains
--Definitions and Examples
--Multi-step Transition Probabilities
--Classification of States
--Limit Behavior
--Some Special Examples
--One Step Calculations
--Infinite State Spaces
--Proofs of Convergence Theorems

2   Martingales
--Conditional Expectation
--Examples of Martingales
--Optional Stopping Theorem

3   Poisson Processes
--Exponential Distribution
--Defining the Poisson Process
--Compund Poisson Processes
--Thinning and Superposition
--Spatial Poisson Processes

4   Continuous-time Markov Chains
--Definitions and Examples
--Computing the Transition Probability
--Limiting Behavior
--Queueing Chains
--Queueing Networks
--Closed Queueing Networks

5   Renewal Theory
--Basic Definitions
--Laws of Large Numbers
--Applications to Queueing Theory
--Age and Residual Life

6   Brownian Motion
--Basic Definitions
--Markov Property, Reflection Principle
--Martingales, Hitting Times
--Option Pricing in Discrete Time
--The Black-Scholes Formula
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