Probability theory : an analytic view / Daniel W. Stroock.

Format:

Book

Author/Creator:

Stroock, Daniel W., author.

Language:

English

Subjects (All):

Probabilities.

Physical Description:

1 online resource (xxi, 527 pages) : digital, PDF file(s).

Edition:

Second edition.

Place of Publication:

Cambridge : Cambridge University Press, 2011.

Language Note:

English

Summary:

This second edition of Daniel W. Stroock's text is suitable for first-year graduate students with a good grasp of introductory, undergraduate probability theory and a sound grounding in analysis. It is intended to provide readers with an introduction to probability theory and the analytic ideas and tools on which the modern theory relies. It includes more than 750 exercises. Much of the content has undergone significant revision. In particular, the treatment of Levy processes has been rewritten, and a detailed account of Gaussian measures on a Banach space is given. The first part of the book deals with independent random variables, Central Limit phenomena, and the construction of Levy processes, including Brownian motion. Conditioning is developed and applied to discrete parameter martingales in Chapter 5, Chapter 6 contains the ergodic theorem and Burkholder's inequality, and continuous parameter martingales are discussed in Chapter 7. Chapter 8 is devoted to Gaussian measures on a Banach space, where they are treated from the abstract Wiener space perspective. The abstract theory of weak convergence is developed in Chapter 9, which ends with a proof of Donsker's Invariance Principle. The concluding two chapters contain applications of Brownian motion to the analysis of partial differential equations and potential theory.

Contents:

Cover; Half-title; Title; Copyright; Dedication; Contents; Preface; Table of Dependence; Chapter 1 Sums of Independent Random Variables; Chapter 2 The Central Limit Theorem; Chapter 3 In nitely Divisible Laws; Chapter 4 Levy Processes; Chapter 5 Conditioning and Martingales; Chapter 6 Some Extensions and Applications of Martingale Theory; Chapter 7 Continuous Parameter Martingales; Chapter 8 Gaussian Measures on a Banach Space; Chapter 9 Convergence of Measures on a Polish Space; Chapter 10 Wiener Measure and Partial Differential Equations; Chapter 11 Some Classical Potential Theory; Notation

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-107-21671-0

1-283-06630-0

9786613066305

0-511-97424-8

1-139-01162-6

1-139-01188-X

1-139-01109-X

1-139-01082-4

1-139-01135-9

OCLC:

707068431