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Brownian Motion and Stochastic Calculus : Graduate Texts in Mathematics - Ioannis Karatzas

Brownian Motion and Stochastic Calculus

Graduate Texts in Mathematics

Paperback Published: August 1991
ISBN: 9780387976556
Number Of Pages: 470

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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.

Industry 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

Martingales, Stopping Times, and Filtrations
Brownian Motion
Stochastic Integration
Brownian Motion and Partial Differential Equations
Stochastic Differential Equations
LFvy's Theory of Brownian Local Time
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387976556
ISBN-10: 0387976558
Series: Graduate Texts in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 470
Published: August 1991
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.11 x 15.49  x 2.79
Weight (kg): 0.7
Edition Number: 2
Edition Type: Revised

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