文档介绍：Probability Methods
for Approximations in Stochastic Control
and for Elliptic Equations
Harold J. Kushner
DEPARTMENTS OF APPLIED MATHEMATICS
AND ENGINEERING
BROWN UNIVERSITY
PROVIDENCE, RHODE ISLAND
ACADEMIC PRESS New York San Francisco London 1977
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Library of Congress Cataloging in Publication Data
Kushner, Harold Joseph, Date
Probability methods for approximations in stochastic
control and for elliptic equations.
(Mathematics in science and engineering ; v. 129)
1. Control theory. 2. Differential equations,
Elliptic. 3. Approximation theory. 4. Probabilities.
I. Title. 11. Series.
76-13942
ISBN 0-12-430140-1
AMS (MOS) 1970 Subject Classifications: 93E20,93E25, 65M10,
60B10, and 90C40
PRINTED IN THE UNITED STATES OF AMERICA
To
Linda, Diana, and Nina
Contents
Preface xi
Acknowledgmtnb xvii
The Wimer Ptoc:euc$ 2
Martinples s
Markov Cs 7
Stochastie lntqrals 9
Stoclla51ic Ditrerential Equations 17
Chapter 2. Weak C..vergence of Prollebility Measures
Probability Measures on the Real Line. Real-Valued Random Variables 2S
ProbabiiHy Measures on Metric Spaces 26
The Spaces C"[o. ~) of Continuous Functions 28
The Space D"'(o. II] 29
Weak on Other Spaces 34
rii
viii CONTENTS
Chapter 3. Markov Quoins •nd Control Problems wirh Markov
Quoin Models
3. 1 Equations Satisfied by f