Measure Theory and Probability Theory / Edition 1

Measure Theory and Probability Theory / Edition 1

by Krishna B. Athreya, Soumendra N. Lahiri
     
 

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ISBN-10: 1441921915

ISBN-13: 9781441921918

Pub. Date: 11/23/2010

Publisher: Springer New York

This is a graduate level textbook on measure theory and probability theory. It presents the main concepts and results in measure theory and probability theory in a simple and easy-to-understand way. It further provides heuristic explanations behind the theory to help students see the big picture. The book can be used as a text for a two semester sequence of courses

Overview

This is a graduate level textbook on measure theory and probability theory. It presents the main concepts and results in measure theory and probability theory in a simple and easy-to-understand way. It further provides heuristic explanations behind the theory to help students see the big picture. The book can be used as a text for a two semester sequence of courses in measure theory and probability theory, with an option to include supplemental material on stochastic processes and special topics. Prerequisites are kept to the minimal level and the book is intended primarily for first year Ph.D. students in mathematics and statistics.

Product Details

ISBN-13:
9781441921918
Publisher:
Springer New York
Publication date:
11/23/2010
Series:
Springer Texts in Statistics Series
Edition description:
Softcover reprint of hardcover 1st ed. 2006
Pages:
619
Product dimensions:
6.14(w) x 9.21(h) x 1.29(d)

Table of Contents

Measures and Integration: An Informal Introduction.- Measures.- Integration.- Lp-Spaces.- Differentiation.- Product Measures, Convolutions, and Transforms.- Probability Spaces.- Independence.- Laws of Large Numbers.- Convergence in Distribution.- Characteristic Functions.- Central Limit Theorems.- Conditional Expectation and Conditional Probability.- Discrete Parameter Martingales.- Markov Chains and MCMC.- Stochastic Processes.- Limit Theorems for Dependent Processes.- The Bootstrap.- Branching Processes.

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