9780486814889

Probability Theory Third Edition

by
  • ISBN13:

    9780486814889

  • ISBN10:

    0486814882

  • Edition: 3rd
  • Format: Paperback
  • Copyright: 2017-07-18
  • Publisher: Dover Publications

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Summary

"Every serious probabilist should, and doubtless will, possess a copy of this important work. Loève is to be complimented on completing his Herculean task at a uniformly high level of elegance." ― Journal of the American Statistical Association
"This is a very scholarly book in the best tradition of analysis. Nothing else of this type exists for the benefit of the serious student of the subject and it is safe to predict that it will remain a standard compendium for many years to come." ― S. Vajda in Zentralblatt für Mathematik
In the decades following its 1963 publication, this volume served as the standard advanced text in probability theory. Geared toward graduate students and professionals in the field of probability and statistics, the treatment offers extensive introductory material and is suitable for an undergraduate course in probability theory. The first four chapters cover notions of measure theory plus general concepts and tools of probability theory. Subsequent chapters explore sums of independent random variables, the central limit problem, conditioning, independence and dependence, ergodic theorems, and second order properties. The final two chapters examine foundations, martingales, and decomposability as well as Markov processes.

Author Biography

Michel Loève (1907–79) was born in Jaffa, Israel, and studied advanced mathematics in France. A Holocaust survivor of the Drancy concentration camp, Loève emigrated to the United States and was Professor of Mathematics at Berkeley from 1948, adding the titles of Professor of Statistics in 1955 and Professor Emeritus in 1974.

Table of Contents

Contents:
Introductory: Elementary Probability Theory
I. Intuitive Background
II. Axioms, Independence and the Bernoulli Case
III. Dependence and Chains
Part One: Notions of Measure Theory
Chapter One: Sets, Spaces, and Measures
Chapter Two: Measurable Functions and Integration
Part Two: General Concepts and Tools of Probability Theory
Chapter Three: Probability Concepts
Chapter Four: Distribution Functions and Characteristic Functions
Part Three: Independence
Chapter Five: Sums of Independent Random Variables
Chapter Six: Central Limit Problem
Part Four: Dependence
Chapter Seven: Conditioning
Chapter Eight: From Independence to Dependence
Chapter Nine: Ergodic Theorems
Chapter Ten: Second Order Properties
Part Five: Elements of Random Analysis
Chapter Eleven: Foundations, Martingales, and Decomposability
Chapter Twelve: Markov Processes
Bibliography
Index

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