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Brownian Motion and Stochastic Calculus

  • Textbook
  • © 1998
  • Latest edition

Overview

  • A perennial best-seller, now in its fourth printing
  • Brownian motion is currently a hot topic in mathematics
  • Karatzas is one of the leaders in the field of stochastics and finance

Part of the book series: Graduate Texts in Mathematics (GTM, volume 113)

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About this book

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.

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Keywords

Table of contents (6 chapters)

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

Authors and Affiliations

  • Departments of Mathematics and Statistics, Columbia University, New York, USA

    Ioannis Karatzas

  • Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, USA

    Steven E. Shreve

Bibliographic Information

  • Book Title: Brownian Motion and Stochastic Calculus

  • Authors: Ioannis Karatzas, Steven E. Shreve

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-0949-2

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1998

  • Softcover ISBN: 978-0-387-97655-6Published: 16 August 1991

  • eBook ISBN: 978-1-4612-0949-2Published: 27 March 2014

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 2

  • Number of Pages: XXIII, 470

  • Topics: Probability Theory and Stochastic Processes, Classical Mechanics

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