Stochastic Processes A Survey of the Mathematical Theory
This book is the result of lectures which I gave dur ing the academic year 1972-73 to third-year students a~ Aarhus University in Denmark. The purpose of the book, as of the lectures, is to survey some of the main themes in the modern theory of stochasti
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Lawrence Sirovich Division of Applied Mathematics Brown University Providence. R.I. 02912
Joseph P. LaSalle
Division of Applied Mathematics Lefschetz Center for Dynamical Systems Providence. R.I. 02912
ADVISORS H. Cabannes University of Paris-VI M. Ghil New York University J.K. Hale Brown University
J. Keller Stanford University J. Marsden Univ. of California at Berkeley G.B. Whitham California Insl. of Technology
EDITORIAL STATEMENT The mathematization of all sciences. the fading of traditional scientific boundaries. the impact of computer technology. the growing importance of mathematicalcomputer modelling and the necessity of scientific planning all create the need both in education and research for books that are introductory to and abreast of these developments. The purpose of this series is to provide such books. suitable for the user of mathematics. the mathematician interested in applications. and the student scientist. In particular. this series will provide an outlet for material less formally presented and more anticipatory of needs than finished texts or monographs. yet of immediate interest because of the novelty of its treatment of an application or of mathematics being applied or lying close to applications. The aim of the series is. through rapid publication in an attractive but inexpensive format. to make material of current interest widely accessible. This implies the absence of excessive generality and abstraction. and unrealistic idealization. but with quality of exposition as a goal. Many of the books will originate out of and will stimulate the development of new undergraduate and graduate courses in the applications of mathematics. Some of the books will present introductions to new areas of research. new applications and act as signposts for new directions in the mathematical sciences. This series will often serve as an intermediate stage of the publication of material which. through exposure here. will be further developed and refined. These will appear in conventional format and in hard cover.
MANUSCRIPTS The Editors welcome all inquiries regarding the submission of manuscripts for the series. Final preparation of all manuscripts will take place in the editorial offices of the series in the Division of Applied Mathematics. Brown University. Providence. Rhode Island. SPRINGER-VERLAG NEW YORK INC .. 175 Fifth Avenue. New York. N. Y. 10010
Applied Mathematical Sciences
I Volume 23
John Lamperti
Stochastic Processes A Survey of the Mathematical Theory
Springer-Verlag New York Heidelberg Berlin
John Lamperti Department of Mathematics Dartmouth College Hanover. New Hampshire 03755
AMS Subject Classifications:
60-01. 60Gxx. 60Jxx
Library of Congress Cataloging in Publication Data Lamperti. John. Stochastic processes. (Applied mathematical sciences ; v. 23) Bibliography: p. Includes index. 1. Stochastic processes. 2. Stationary processes. 3. Markov processes. I. Title. I I. Series. QAl.A647 vol. 23 [QA274] 5l0'.8s [519.2) 77-24321 All rights reserved. No part of this book may be
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