Introduction to stochastic processes
 Responsibility
 Gregory F. Lawler
 Edition
 2nd ed
 Imprint
 Boca Raton : Chapman & Hall/CRC, 2006
 Physical description
 1 online resource (xiii, 234 pages)
Online
Available online
 ProQuest Ebook Central Access limited to 3 simultaneous users
Course reserve
 Course
 MATH13601  Stochastic Processes
 Instructor(s)
 Dembo, Amir
More options
Description
Creators/Contributors
 Author/Creator
 Lawler, Gregory F., 1955
 Contributor
 ProQuest (Firm)
Contents/Summary
 Bibliography
 Includes bibliographical references and index
 Contents

 Preface to Second Edition Preface to First Edition PRELIMINARIES Introduction Linear Differential Equations Linear Difference Equations Exercises FINITE MARKOV CHAINS Definitions and Examples LargeTime Behavior and Invariant Probability Classification of States Return Times Transient States Examples Exercises COUNTABLE MARKOV CHAINS Introduction Recurrence and Transience Positive Recurrence and Null Recurrence Branching Process Exercises CONTINUOUSTIME MARKOV CHAINS Poisson Process Finite State Space BirthandDeath Processes General Case Exercises OPTIMAL STOPPING Optimal Stopping of Markov Chains Optimal Stopping with Cost Optimal Stopping with Discounting Exercises MARTINGALES Conditional Expectation Definition and Examples Optional Sampling Theorem Uniform Integrability Martingale Convergence Theorem Maximal Inequalities Exercises RENEWAL PROCESSES Introduction Renewal Equation Discrete Renewal Processes M/G/1 and G/M/1 Queues Exercises REVERSIBLE MARKOV CHAINS Reversible Processes Convergence to Equilibrium Markov Chain Algorithms A Criterion for Recurrence Exercises BROWNIAN MOTION Introduction Markov Property Zero Set of Brownian Motion Brownian Motion in Several Dimensions Recurrence and Transience Fractal Nature of Brownian Motion Scaling Rules Brownian Motion with Drift Exercises STOCHASTIC INTEGRATION Integration with Respect to Random Walk Integration with Respect to Brownian Motion Ito's Formula Extensions if Ito's Formula Continuous Martingales Girsanov Transformation FeynmanKac Formula BlackScholes Formula Simulation Exercises Suggestions for Further Reading Index.
 (source: Nielsen Book Data)
 Summary

Emphasizing fundamental mathematical ideas rather than proofs, Introduction to Stochastic Processes, Second Edition provides quick access to important foundations of probability theory applicable to problems in many fields. Assuming that you have a reasonable level of computer literacy, the ability to write simple programs, and the access to software for linear algebra computations, the author approaches the problems and theorems with a focus on stochastic processes evolving with time, rather than a particular emphasis on measure theory. For those lacking in exposure to linear differential and difference equations, the author begins with a brief introduction to these concepts. He proceeds to discuss Markov chains, optimal stopping, martingales, and Brownian motion. The book concludes with a chapter on stochastic integration. The author supplies many basic, general examples and provides exercises at the end of each chapter. New to the Second Edition: Expanded chapter on stochastic integration that introduces modern mathematical finance Introduction of Girsanov transformation and the FeynmanKac formula Expanded discussion of Ito's formula and the BlackScholes formula for pricing options New topics such as Doob's maximal inequality and a discussion on self similarity in the chapter on Brownian motion Applicable to the fields of mathematics, statistics, and engineering as well as computer science, economics, business, biological science, psychology, and engineering, this concise introduction is an excellent resource both for students and professionals.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2006
 Reproduction
 Electronic reproduction. Ann Arbor, MI Available via World Wide Web
 ISBN
 9781482286113 (electronic bk.)
 1482286114 (electronic bk.)
 158488651X
 9781584886518
 9781315273600 (ebook ; PDF)
 1315273608 (ebook ; PDF)