An Introduction to Measure-Theoretic Probability - Hardcover

George G. Roussas

Hardcover

ISBN 10: 0128000422 ISBN 13: 9780128000427

Publisher: Academic Press, 2014

Synopsis

An Introduction to Measure-Theoretic Probability, Second Edition, employs a classical approach to teaching students of statistics, mathematics, engineering, econometrics, finance, and other disciplines measure-theoretic probability. This book requires no prior knowledge of measure theory, discusses all its topics in great detail, and includes one chapter on the basics of ergodic theory and one chapter on two cases of statistical estimation. There is a considerable bend toward the way probability is actually used in statistical research, finance, and other academic and nonacademic applied pursuits.

• Provides in a concise, yet detailed way, the bulk of probabilistic tools essential to a student working toward an advanced degree in statistics, probability, and other related fields
• Includes extensive exercises and practical examples to make complex ideas of advanced probability accessible to graduate students in statistics, probability, and related fields
• All proofs presented in full detail and complete and detailed solutions to all exercises are available to the instructors on book companion site

About this title

Review:

"...a very thorough discussion of many of the pillars of the subject, showing in particular how 'measure theory with total measure one' is just the tip of the iceberg...It’s quite a book." --MAA.org, An Introduction to Measure-Theoretic Probability

"This second edition employs a classical approach to teaching students of statistics, mathematics, engineering, econometrics, finance, and other disciplines measure-theoretic probability...requires no prior knowledge of measure theory, discusses all its topics in great detail, and includes one chapter on the basics of ergodic theory and one chapter on two cases of statistical estimation." --Zentralblatt MATH 1287-1

"...provides basic tools in measure theory and probability, in the classical spirit, relying heavily on characteristic functions as tools without using martingale or empirical process methods. A well-written book. Highly recommended [for] graduate students; faculty." --CHOICE

Based on the material presented in the manuscript, I would without any hesitation adopt the published version of the book. The topics dealt are essential to the understanding of more advanced material; the discussion is deep and it is combined with the use of essential technical details. It will be an extremely useful book. In addition it will be a very popular book." --Madan Puri, Indiana University

"Would likely use as one of two required references when I teach either Stat 709 or Stat 732 again. Would also highly recommend to colleagues. The author has written other excellent graduate texts in mathematical statistics and contiguity and this promises to be another. This book could well become an important reference for mathematical statisticians." --Richard Johnson, University of Wisconsin

"The author has succeeded in making certain deep and fundamental ideas of probability and measure theory accessible to statistics majors heading in the direction of graduate studies in statistical theory." --Doraiswamy Ramachandran, California State University

About the Author:

George G. Roussas received his B.A. in Mathematics at the University of Athens, Greece, and his Ph.D. in Statistics at the University of California, Berkeley. Roussas is currently Professor and Associate Dean of Statistics at the University of California, Davis. His teaching career began at the University of Wisconsin, Madison. Then he was a Professor of Applied Mathematics at the University of Patras, Greece, and also served as the Dean of the College of Sciences and as Chancellor of that University. At the University of Crete, Greece, Roussas served as Vice President of Academic Affairs. Roussas has published several books, and had more than 65 research papers published in refereed journals. He is a Fellow of the Institute of Mathematical Statistics, the American Statistical Association, and the Royal Statistical Society, and is an elected member of the International Statistical Institute. Finally, Roussas is the Associate Editor of two journals, Statistics and Probability Letters, and Nonparametric Statistics.

About this edition

• Publisher: Academic Press
• Publication date: 2014
• ISBN 10: 0128000422
• ISBN 13: 9780128000427
• Binding: Hardcover
• Edition number: 2
• Number of pages: 426