Probability and Measure Theory
- 2nd Edition - December 8, 1999
- Latest edition
- Authors: Robert B. Ash, Catherine A. Doleans-Dade
- Language: English
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 extens… Read more
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
Graduate students, faculty, and other professionals in mathematics, statistics, engineering, and economics; also, graduate students and professionals in physics and computer science
Summary of Notation
Fundamentals of Measure and Integration Theory.
Further Results in Measure and Integration Theory.
Introduction to Functional Analysis.
Basic Concepts of Probability.
Conditional Probability and Expectation.
Strong Laws of Large Numbers and Martingale Theory.
The Central Limit Theorem.
Ergodic Theory.
Brownian Motion and Stochastic Integrals.
Fundamentals of Measure and Integration Theory.
Further Results in Measure and Integration Theory.
Introduction to Functional Analysis.
Basic Concepts of Probability.
Conditional Probability and Expectation.
Strong Laws of Large Numbers and Martingale Theory.
The Central Limit Theorem.
Ergodic Theory.
Brownian Motion and Stochastic Integrals.
"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!"—http://www.contingencyanalysis.com
- Edition: 2
- Latest edition
- Published: December 8, 1999
- Language: English
RA
Robert B. Ash
Robert B. Ash as written about, taught, or studied virtually every area of mathematics. His books include Information Theory, Topics in Stochastic Processes, The Calculus Tutoring Book, Introduction to Discrete Mathematics, and A Primer of Mathematics.
Affiliations and expertise
University of Illinois, Urbana-Champaign, U.S.A.CD
Catherine A. Doleans-Dade
Affiliations and expertise
University of Illinois, Urbana-Champaign, U.S.A.