Measure Theory and Probability Theory / Edition 1

Measure Theory and Probability Theory / Edition 1

by Krishna B. Athreya, Soumendra N. Lahiri
     
 

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

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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 introduction1
1Measures9
2Integration39
3L[superscript p]-spaces83
4Differentiation113
5Product measures, convolutions, and transforms147
6Probability spaces189
7Independence219
8Laws of large numbers237
9Convergence in distribution287
10Characteristic functions317
11Central limit theorems343
12Conditional expectation and conditional probability383
13Discrete parameter martingales399
14Markov chains and MCMC439
15Stochastic processes487
16Limit theorems for dependent processes509
17The bootstrap533
18Branching processes561
AAdvanced calculus : a review573

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