Introduction to Stochastic Processes

by Gregory F. Lawler

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 Feynman-Kac formula
Expanded discussion of Itô's formula and the Black-Scholes 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.

Genres: Mathematics, Nonfiction

248 pages, Kindle Edition

First published July 1, 1995

Reviews

[Saman · Rating 4 out of 5]

Stochastic processes is the mathematical study of processes which have some random elements in it. Like what happens in a gambling match or in biology, the probability of survival or extinction of species. The book starts from easy questions, specially when the time is discrete, later it goes to continuous time problems and Brownian motions. One of the best books in this area, I don't remember any line to be vague or hard to understand. It is attractive both from pure perspective and practical viewpoint.

[Dmitri · Rating 5 out of 5]

This is a great introductory book for stochastic calculus. Unlike most books on stochastics, this one does not require the knowledge of measure theory, but does require some fundamental knowledge of difference equations and linear algebra. The book mainly covers the topic of Markov chains in discrete and continuous settings, but does cover a bit of Ito calculus too (just the basics, though). It's a very accessible text, though sometimes its explanations go a bit too far in terms of theory - something that's difficult to avoid, I guess. It is, by now, an out-of-print text that's very difficult to get a hold of.