Martingales and Stochastic Integrals I
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284 Paul-Andre Meyer Universit6 de Strasbourg, Strasbourg/France
Martingales and Stochastic integrals I
Springer-Verlag Berlin. Heidelberg- New York 1972
A M S S u b j e c t Classifications (1970): p r i m a r y : 6 0 G 4 5 secondary: 60 H 05
I S B N 3"540-05983-0 S p r i n g e r - V e r l a g B e r l i n • H e i d e l b e r g • N e w Y o r k I S B N 0-387-05983-0 S p r i n g e r - V e r t a g N e w Y o r k • H e i d e l b e r g - B e r l i n This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 5'4 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin - Heidelberg 1972. Library of Congress Catalog Card Number 72-88111. Printed in Germany. Offsetdruck: Julius Beltz, Hemsbach/Bergstr.
Introduction This volume contains a preliminary version ( the second draft) of the first two chapters of a book on martingales and stochastic integrals. If the following chapters are ever to be written, it will be as a joint work with C1. Dellacherie
: we plan to write at last
the chapters on continuous time martingales in 1972-73, and to publish them in the Lecture Notes series. The next installment then will be on stochastic integrals. Formal publication will probably take place much later, and at that time the first chapters will probably ( and hopefully ) be obsolete. There exist several texts on martingale theory, standard or specialized ; at least three more are forthcoming, which should be rather outstanding. On the other hand, nothing exists in book form on the general theory of stochastic integrals, and our emphasis will be on that side. The book would just have been called that way, hadn't it been that the title already belongs to the wonderful little book by McKean ( which however deals only with the sample continuous case ). Accordingly, I convergence, but
have mentioned only the most standard facts about I tried to be rather complete about transforms, qua-
dratic variation, etc. The point of view here is quite different from that of my own chapters Eli on martingale theory, which tried to follow the ideas of probabilistic potential theory. Part of the material was taught ( in Gerglish ) in 1970/71 at the Albert-Ludwig University at Freiburg i/Breisgau. During that year I was subsidized by the Deutsche Forschungsgemeinschaft, and during the following Wintersemester by the University itself. I am most grateful to them for this generous and pleasant hospitality. This stay in Germany, and the idea of writing the book for a German publisher, explain why I didn't write in French . Some English speaking friends complained about it. Let them face the facts : there is a worldwide speculation on the devaluation of English. For corre
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