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Overview
Probability and Measure Theory, Second Edition, is a text for a graduate-level course in probability that includes essential background topics in analysis. It provides extensive coverage of conditional probability and expectation, strong laws of large numbers, martingale theory, the central limit theorem, ergodic theory, and Brownian motion.
• Clear, readable style
• Solutions to many problems presented in text
• Solutions manual for instructors
• Material new to the second edition on ergodic theory, Brownian motion, and convergence theorems used in statistics
• No knowledge of general topology required, just basic analysis and metric spaces
• Efficient organization
Audience: Graduate students, faculty, and other professionals in mathematics, statistics, engineering, and economics; also, graduate students and professionals in physics and computer science.
Synopsis
No date is noted for the first edition, published as Real Analysis and Probability, but it has been used for graduate courses in measure and probability in mathematics and statistics departments that are often taken by students of engineering. Ash and Catherine A. Koléans-Dade have added one chapter that discusses ergodic theory far enough that its connections with information theory are clear, and other that treats the one-dimensional Brownian motion in detail then introduces stochastic intervals and the Ito differentiation formula. They are in Urbana, so presumably at the University of Illinois there.
Annotation c. Book News, Inc., Portland, OR (booknews.com)
Editorials
From the Publisher
Published ReviewsAs reviewed at http://www.contingencyanalysis.com
"There are numerous probability texts on the market, which makes choosing one difficult. If you are a financial professional who knows basic probability theory, but wants to take the next step in sophistication, this is the essential text. It introduces basic measure theory and functional analysis, and then delves into probability. The writing is clear and highly accessible. The choice of topics is perfect for financial engineers or financial risk managers: martingales, the inversion theorem, the central limit theorem, Brownian motion and stochastic integrals. I can't praise this book enough. It is exceptional!"