Introduction to Stochastic Integration.pdf

Universitext
Editorial Board
(North America):
S. Axler
. Ribet
Hui-Hsiung Kuo
Introduction to
Stochastic Integration
Hui-Hsiung Kuo
Department of Mathematics
Louisiana State University
Baton Rouge, LA 70803-4918
USA
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Editorial Board
(North America):
S. Axler . Ribet
Mathematics Department Mathematics Department
San Francisco State University University of California at Berkeley
San Francisco, CA 94132 Berkeley, CA 94720-3840
USA USA
******@ ******@
Mathematics Subject Classification (2000): 60-XX
Library of Congress Control Number: 2005935287
ISBN-10: 0-387-28720-5 Printed on acid-free paper.
ISBN-13: 978-0387-28720-1
© 2006 Springer Science+Business Media, Inc.
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Printed in the United States of America. (EB)
987654321
Dedicated to Kiyosi Itˆo,
and in memory of
his wife Shizue Itˆo
Preface
In the Leibniz–Newton calculus, one learns the differentiation and integration
of deterministic functions. A basic theorem in differentiation is the chain rule,
which gives the derivative of posite of two differentiable functions. The
chain rule, when written in an indefinite integral form, yields the method of
substitution. In advanced calculus, the Riemann–Stieltjes integr