Brownian Motion and Stochastic Calculus

ISBN-10: 0387976558
ISBN-13: 9780387976556
Edition: 2nd 1998 (Revised)
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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  More...

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Book details

List price: $64.95
Edition: 2nd
Copyright year: 1998
Publisher: Springer
Publication date: 8/25/2004
Binding: Paperback
Pages: 470
Size: 6.25" wide x 9.50" long x 1.00" tall
Weight: 1.738
Language: English

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.

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

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