ENGLISH

Brownian motion and stochastic calculus

By Ioannis Karatzas , Steven E. Shreve

Book information

Publisher
Springer
Year
1991
ISBN
9780387976556, 9783540976554, 0387976558, 3540976558
LCC
QA274.75 .K37 1991
Open Library ID
OL1543776M
Language
english
Format
DJVU
Filesize
3 MB (3083666 bytes)
Series
Graduate Texts in Mathematics
Edition
2nd
Pages
488\488
Library
Kolxo3
DPI
300
Scanned
yes
Time added
2010-07-29 05:14:56

Description

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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