Brownian Motion and Stochastic Calculus

Ioannis Karatzas, Steven E. Shreve - Collection Graduate Texts in Mathematics

470 pages, parution le 01/01/1998

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Résumé

A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing 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, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The 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 whole is backed by a large number of problems and exercises.

Written for:

Graduate mathematics student; mathematicians; people in finance

L'auteur - Steven E. Shreve

Steven E. Shreve is Co-Founder of the Carnegie Mellon MS Program in Computational Finance and winner of the Carnegie Mellon Doherty Prize for sustained contributions to education.

Sommaire

Martingales, Stopping Times, and Filtrations
Brownian Motion
Stochastic Integration
Brownian Motion and Partial Differential Equations
Stochastic Differential Equations
Lévy's Theory of Brownian Local Time

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Ioannis Karatzas, Steven E. Shreve
Collection	Graduate Texts in Mathematics
Parution	01/01/1998
Nb. de pages	470
Couverture	Relié
Intérieur	Noir et Blanc
EAN13	9780387976556
ISBN13	978-0-387-97655-6