,Graduate Texts in Mathematics 113
Editorial Board
S. Axler F.W. Gehring K.A. Ribet
,Ioannis Karatzas Steven E. Shreve
Brownian Motion
and Stochastic Calculus
Second Edition
With 10 Illustrations
~ Springer
, Ioannis Karatzas Steven E. Shreve
Departments of Mathematics Department of Mathematical Sciences
and Statistics Carnegie Mellon University
Columbia University Pittsburgh, PA 15213
New York, NY 10027 USA
USA
Editorial Board
S. Axler F. W. Gehring
Mathematics Department Mathematics Department
San Francisco State University East Hali
San Francisco, CA 94132 University of Michigan
USA Ann Arbor, MI 48109-1109
USA
K.A. Ribet
Mathematics Department
University of California at Berkeley
Berkeley, CA 94720-3840
USA
Mathematics Subject Classification (2000): 60G07, 60H05
Library of Congress Cataloging-in-Publication Data
Karatzas, loannis.
8rownian motion and stochastic calculus / loannis Karatzas, Steven
E. Shreve.-2nd ed.
p. cm. - (Graduate texts in mathematics; 113)
Includes bibliographical references and index.
ISBN 978-0-387-97655-6 ISBN 978-1-4612-0949-2 (eBook)
DOI 10.1007/978-1-4612-0949-2
1. 8rownian motion processes. 2. Stochastic analysis.
1. Shreve, Steven E. [1. Title. III. Series.
QH274.75.K37 1991
530.4 '75-dc20 91-22775
The present volume is the corrected softcover second edition of the previously published hardcover
first edition (ISBN 978-0-387-97655-6).
ISBN 978-0-387-97655-6 Printed on acid-free paper.
© 1998,1991 Springer Science+BusinessMedia New York
Originally published by Springer Science+Business Media, Inc. in 1998
AII rights reserved. This work may not be translated or copied in whole or in part without the written
permission of the publisher Springer Science+Business Media, LLC,
except for brief excerpts in connection with reviews or scholarly analysis. Vse in
connection with any form of information storage and retrieval, electronic adaptation, computer
software, or by similar or dissimilar methodology now known or hereafter developed is forbidden.
The use in this publication of trade names, trademarks, service marks and similar terms, even if they
are not identified as such. is not to be taken as an expression of opinion as to whether or not they are
subject to proprietary rights.
9
springeronlioe.com
Editorial Board
S. Axler F.W. Gehring K.A. Ribet
,Ioannis Karatzas Steven E. Shreve
Brownian Motion
and Stochastic Calculus
Second Edition
With 10 Illustrations
~ Springer
, Ioannis Karatzas Steven E. Shreve
Departments of Mathematics Department of Mathematical Sciences
and Statistics Carnegie Mellon University
Columbia University Pittsburgh, PA 15213
New York, NY 10027 USA
USA
Editorial Board
S. Axler F. W. Gehring
Mathematics Department Mathematics Department
San Francisco State University East Hali
San Francisco, CA 94132 University of Michigan
USA Ann Arbor, MI 48109-1109
USA
K.A. Ribet
Mathematics Department
University of California at Berkeley
Berkeley, CA 94720-3840
USA
Mathematics Subject Classification (2000): 60G07, 60H05
Library of Congress Cataloging-in-Publication Data
Karatzas, loannis.
8rownian motion and stochastic calculus / loannis Karatzas, Steven
E. Shreve.-2nd ed.
p. cm. - (Graduate texts in mathematics; 113)
Includes bibliographical references and index.
ISBN 978-0-387-97655-6 ISBN 978-1-4612-0949-2 (eBook)
DOI 10.1007/978-1-4612-0949-2
1. 8rownian motion processes. 2. Stochastic analysis.
1. Shreve, Steven E. [1. Title. III. Series.
QH274.75.K37 1991
530.4 '75-dc20 91-22775
The present volume is the corrected softcover second edition of the previously published hardcover
first edition (ISBN 978-0-387-97655-6).
ISBN 978-0-387-97655-6 Printed on acid-free paper.
© 1998,1991 Springer Science+BusinessMedia New York
Originally published by Springer Science+Business Media, Inc. in 1998
AII rights reserved. This work may not be translated or copied in whole or in part without the written
permission of the publisher Springer Science+Business Media, LLC,
except for brief excerpts in connection with reviews or scholarly analysis. Vse in
connection with any form of information storage and retrieval, electronic adaptation, computer
software, or by similar or dissimilar methodology now known or hereafter developed is forbidden.
The use in this publication of trade names, trademarks, service marks and similar terms, even if they
are not identified as such. is not to be taken as an expression of opinion as to whether or not they are
subject to proprietary rights.
9
springeronlioe.com
