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Introduction to Stochastic Processes, First Edition

Probability Series

Chapman & Hall



G.F. Lawler, Professor of Mathematics, Duke University, USA

Hardback © 1995
ISBN: 0-41299-511-5
Publication Status: THIS BOOK HAS JUST BEEN REPRINTED (OCT 96) AND COPIES SHOULD BE AVAILABLE
Readership: graduate students and advanced undergraduates in engineering, statistics, biological and physical sciences, economics and business as well as mathematics; researchers in stochastic processes

This textbook provides a concise and informal introduction to stochastic processes evolving with time. Emphasizing fundamental mathematical ideas rather than proofs or detailed applications, it is an ideal text for a first course in stochastic processes without measure theory, requiring only a calculus-based undergraduate probability course and a course in linear algebra. Introduction to Stochastic Processes will be useful for students in mathematics, statistics, computer science, economics, business, biological sciences, psychology, physics and engineering. In a comprehensive and modern treatment, the author: * begins with standard material on finite Markov chains, emphasizing the relationship between the convergence to equilibrium and the size of the eigenvalues of the stochastic matrix * introduces infinite state space, including the notions of transcience, null recurrence and positive recurrence, as well as a discussion of branching processes * examines three main types of continuous-time Markov chains-Poisson process, finite state space and birth-and -death processes-and explores optimal stopping of Markov chains * provides a solid introduction to martingales, including conditional expectation, the optimal sampling theorem and the martingale convergence theorem * discusses renewal processes and topics in the realm of reversible Markov chains, including Markov chain algorithms * presents an introduction to Brownian motion, both multidimensional and one-dimensional, as well as a brief discussion of stochastic integration

Published in English , First Published in the EU July 1995

Size: 176 pages, Dimensions: 229x153 mm 6x9 inches


US List Price: US $49.95
UK/European Community List Price: £32.00

Table of Contents:

  • Preliminaries. Introduction, Linear differential equations, Linear difference equations, exercises.
  • Finite Markov chains. Definitions and examples, Long-range behavior and invariant probability, Classification of States, Return times. Transient states, Examples, Exercises.
  • Countable Markov chains. Introduction, Recurrence and transience, Positive recurrence and null recurence, Branching process, exercises. Continuous-time Markov chains. Poisson process, Finite state space, Birth-and-death 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, 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, Brownian motion with drift, Exercises.
  • Stochastic integration. Integration with respect to random walk, Integration with respect to brownian motion, Ito's formula, Simulation, Exercises.
  • Index.