Martingales and stochastic analysis

Martingales and Stochastic Analysis

SERIES ON MULTIVARIATE ANALYSIS Editor: M M Rao

Forthcoming Vol. 2: Mathematical Methods on Sample Surveys H. F- Tucker

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Analysis Vol. 1 —

MARTINGALES AND

STOCHASTIC ANALYSIS J.Yeh Department oj Mathematics University oj California, Irvine

World Scientific

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Library of of Congress Congress Cataloging-in-Publication Cataloging-in-Publication Data Data Library Yeh, James. Martingales and stochastic analysis / James Yeh. vol. 1) 1) p. cm. -- (Series on multivariate analysis ; vol. Includes bibliographical references and index. ISBN 981022477X 1. Martingales (Mathematics) 2. Stochastic analysis. II. Series. QA274.5.Y44 1995 519.2'87-dc20

I. Title. 95-42874 CIP

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Material

Preface This monograph is an introduction to martingales and stochastic analysis assuming only real analysis and some basic concepts in probability theory. Stochastic independence, con­ ditional expectation, and regular conditional probability are included in the appendix. In writing this monograph I strove for clarity and precision at the cost of concision. Details of proofs are worked out for readability and for reference. Chapter 1 begins with a collection of theorems concerning