Graduate Texts in Mathematics

Brownian Motion and Stochastic Calculus

Authors: Karatzas, Ioannis, Shreve, Steven

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About this Textbook

This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization).

This book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The text is complemented by a large number of problems and exercises.

Reviews

Second Edition

I. Karatzas and S.E. Shreve

Brownian Motion and Stochastic Calculus

"A valuable book for every graduate student studying stochastic process, and for those who are interested in pure and applied probability. The authors have done a good job."—MATHEMATICAL REVIEWS


Table of contents (6 chapters)

  • Martingales, Stopping Times, and Filtrations

    Karatzas, Ioannis (et al.)

    Pages 1-46

  • Brownian Motion

    Karatzas, Ioannis (et al.)

    Pages 47-127

  • Stochastic Integration

    Karatzas, Ioannis (et al.)

    Pages 128-238

  • Brownian Motion and Partial Differential Equations

    Karatzas, Ioannis (et al.)

    Pages 239-280

  • Stochastic Differential Equations

    Karatzas, Ioannis (et al.)

    Pages 281-398

Buy this book

eBook $49.99
price for USA (gross)
  • ISBN 978-1-4612-0949-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $64.95
price for USA
  • ISBN 978-0-387-97655-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Brownian Motion and Stochastic Calculus
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
113
Copyright
1998
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-0949-2
DOI
10.1007/978-1-4612-0949-2
Softcover ISBN
978-0-387-97655-6
Series ISSN
0072-5285
Edition Number
2
Number of Pages
XXIII, 470
Topics