Probability Theory (Paperback)

This volume presents topics in probability theory covered during a first-year graduate course given at the Courant Institute of Mathematical Sciences, USA. The necessary background material in measure theory is developed, including the standard topics, such as extension theorem, construction of measures, integration, product spaces, Radon-Nikodym theorem, and conditional expectation In the first part of the book, characteristic functions are introduced, followed by the study of weak convergence of probability distributions. Then both the weak and strong limit theorems for sums of independent random variables are proved, including the weak and strong laws of large numbers, central limit theorems, laws of the iterated logarithm, and the Kolmogorov three series theorem. The first part concludes with infinitely divisible distributions and limit theorems for sums of uniformly infinitesimal independent random variables. The second part of the book mainly deals with dependent random variables, particularly martingales and Markov chains. Topics include standard results regarding discrete parameter martingales and Doob's inequalities.

General

Imprint:	American Mathematical Society
Country of origin:	United States
Series:	Courant Lecture Notes
Release date:	September 2001
First published:	November 2001
Authors:	S. R. S. Varadhan
Dimensions:	252 x 177 x 10mm (L x W x T)
Format:	Paperback
Pages:	167
ISBN-13:	978-0-8218-2852-6
Categories:	Books > Science & Mathematics > Mathematics > Probability & statistics Books > Science & Mathematics > Mathematics > Applied mathematics > Stochastics
LSN:	0-8218-2852-5
Barcode:	9780821828526

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