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Probability-1 3rd Ed. by A.N.Shiryaev.pdf
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Advanced maths students have been waiting for this, the third edition of a text that deals with one of the fundamentals of their field. This book contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gradually developing more sophisticated subjects, such as random walks and the Kalman-Bucy filter. Examples are discussed in detail, and there are a large number of exercises. This third edition contains new problems and exercises, new proofs, expanded material on financial mathematics, financial engineering, and mathematical statistics, and a final chapter on the history of probability theory.
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Graduate Texts in Mathematics
AlbertN.Shiryaev
Probability-1
Third Edition
Graduate Texts in Mathematics 95
Graduate Texts in Mathematics
Series Editors:
Sheldon Axler
San Francisco State University, San Francisco, CA, USA
Kenneth Ribet
University of California, Berkeley, CA, USA
Advisory Board:
Alejandro Adem, University of British Columbia
David Eisenbud, University of California, Berkeley & MSRI
Irene M. Gamba, The University of Texas at Austin
J.F. Jardine, University of Western Ontario
Jeffrey C. Lagarias, University of Michigan
Ken Ono, Emory University
Jeremy Quastel, University of Toronto
Fadil Santosa, University of Minnesota
Barry Simon, California Institute of Technology
Graduate Texts in Mathematics bridge the gap between passive study and creative
understanding, offering graduate-level introductions to advanced topics in mathe-
matics. The volumes are carefully written as teaching aids and highlight character-
istic features of the theory. Although these books are frequently used as textbooks
in graduate courses, they are also suitable for individual study.
More information about this series at http://www.springer.com/series/136
Albert N. Shiryaev
Probability-1
Third Edition
Translated by R.P. Boas
:
and D.M. Chibisov
123
Albert N. Shiryaev
Department of Probability Theory
and Mathematical Statistics
Steklov Mathematical Institute and
Lomonosov Moscow State University
Moscow, Russia
Translated by R.P. Boas
:
and D.M. Chibisov
ISSN 0072-5285 ISSN 2197-5612 (electronic)
Graduate Texts in Mathematics
ISBN 978-0-387-72205-4 ISBN 978-0-387-72206-1 (eBook)
DOI 10.1007/978-0-387-72206-1
Library of Congress Control Number: 2015942508
Springer New York Heidelberg Dordrecht London
© Springer Science+Business Media New York 1984, 1996, 2016
This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of
the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,
broadcasting, reproduction on microfilms or in any other physical way, and transmission or information
storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology
now known or hereafter developed.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication
does not imply, even in the absence of a specific statement, that such names are exempt from the relevant
protective laws and regulations and therefore free for general use.
The publisher, the authors and the editors are safe to assume that the advice and information in this book
are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or
the editors give a warranty, express or implied, with respect to the material contained herein or for any
errors or omissions that may have been made.
Printed on acid-free paper
Springer Science+Business Media LLC New York is part of Springer Science+Business Media (www.
springer.com)
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