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Probability theory

Author: S R S Varadhan
Publisher: New York : Courant Institute of Mathematical Sciences ; Providence, R.I. : American Mathematical Society, ©2001.
Series: Courant lecture notes in mathematics, 7.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This volume presents topics in probability theory covered during a first-year graduate course given at the Courant Institute of Mathematical Sciences. 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,  Read more...
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Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: S R S Varadhan
ISBN: 0821828525 9780821828526 9781470411374 1470411377
OCLC Number: 956673801
Description: 1 online resource.
Contents: Chapter 1. Measure theory Chapter 2. Weak convergence Chapter 3. Independent sums Chapter 4. Dependent random variables Chapter 5. Martingales Chapter 6. Stationary stochastic processes Chapter 7. Dynamic programming and filtering.
Series Title: Courant lecture notes in mathematics, 7.
Responsibility: S.R.S. Varadhan.

Abstract:

This volume presents topics in probability theory covered during a first-year graduate course given at the Courant Institute of Mathematical Sciences. 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 rando.

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