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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Table of contents (6 chapters)
Keywords
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.
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
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
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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