Stochastic integrals / Henry P. McKean.

Format:

Book

Author/Creator:

McKean, Henry P. (Henry Pratt), 1930- author.

Series:

AMS Chelsea Publishing Series

AMS Chelsea Publishing, v. 353

Language:

English

Subjects (All):

Stochastic integrals.

Brownian movements.

Physical Description:

1 online resource (159 pages)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : AMS Chelsea Publishing, 2005.

Summary:

This little book is a brilliant introduction to an important boundary field between the theory of probability and differential equations.--E. B. Dynkin, Mathematical ReviewsThis well-written book has been used for many years to learn about stochastic integrals. The book starts with the presentation of Brownian motion, then deals with stochastic integrals and differentials, including the famous Itô lemma. The rest of the book is devoted to various topics of stochastic integral equations, including those on smooth manifolds.Originally published in 1969, this classic book is ideal for supplementary reading or independent study. It is suitable for graduate students and researchers interested in probability, stochastic processes, and their applications.

Contents:

Cover

Title page

Dedication

Preface

Contents

List of notations

Stochastic integrals

1 Brownian motion

INTRODUCTION

1.1 GAUSSIAN FAMILIES

1.2 CONSTRUCTION OF THE BROWNIAN MOTION

1.3 SIMPLEST PROPERTIES OF THE BROWNIAN MOTION

1.4 A MARTINGALE INEQUALITY

1.5 THE LAW OF THE ITERATED LOGARITHM

1.6 LEVY'S MODULUS

1.7 SEVERAL-DIMENSIONAL BROWNIAN MOTION

2 Stochastic integrals and differentials

2.1 WIENER'S DEFINITION OF THE STOCHASTIC INTEGRAL

2.2 ITO'S DEFINITION OF THE STOCHASTIC INTEGRAL

2.3 SIMPLEST PROPERTIES OF THE STOCHASTIC INTEGRAL

2.4 COMPUTATION OF A STOCHASTIC INTEGRAL

2.5 A TIME SUBSTITUTION

2.6 STOCHASTIC DIFFERENTIALS AND ITO'S LEMMA

2.7 SOLUTION OF THE SIMPLEST STOCHASTIC DIFFERENTIAL EQUATION

2.8 STOCHASTIC DIFFERENTIALS UNDER A TIME SUBSTITUTION

2.9 STOCHASTIC INTEGRALS AND DIFFERENTIALS FOR SEVERAL-DIMENSIONAL BROWNIAN MOTION

3 Stochastic integral equations ( =1)

3.1 DIFFUSIONS

3.2 SOLUTION OF dx = e(x) db+ f(x) dt FOR COEFFICIENTS WITH BOUNDED SLOPE

3.3 SOLUTION OF dx = e(r) db+ f(r) dt FOR GENERAL COEFFICIENTS BELONGING TO C1(R 1)

3.4 LAMPERTl'S METHOD

3.5 FORWARD EQUATION

3.6 FELLER'S TEST FOR EXPLOSIONS

3.7 CAMERON-MARTIN'S FORMULA

3.8 BROWNIAN LOCAL TIME

3.9 REFLECTING BARRIERS

3.10 SOME SINGULAR EQUATIONS

4 Stochastic integral equations ( ≥2)

4.1 MANIFOLDS AND ELLIPTIC OPERATORS

4.2 WEYL'S LEMMA

4.3 DIFFUSIONS ON A MANIFOLD

4.4 EXPLOSIONS AND HARMONIC FUNCTIONS

4.5 HASMINSKil'S TEST FOR EXPLOSIONS

4.6 COVERING BROWNIAN MOTIONS

4.7 BROWNIAN MOTIONS ON A LIE GROUP

4.8 INJECTION

4.9 BROWNIAN MOTION OF SYMMETRIC MATRICES

4.10 BROWNIAN MOTION WITH OBLIQUE REFLECTION

References

Subject index

Errata

Back Cover.

Notes:

Originally published: New York : Academic Press, 1969, in series: Probability and mathematical statistics, a series of monographs and textbooks, 5.

Includes bibliographical references and index.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

1-4704-3029-0

OCLC:

982022687