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More About This Textbook
Overview
A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore shastic 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 shastic integration and shastic 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 shastic 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.
Editorial Reviews
From the Publisher
Second EditionI. Karatzas and S.E. Shreve
Brownian Motion and Shastic Calculus
"A valuable book for every graduate student studying shastic process, and for those who are interested in pure and applied probability. The authors have done a good job."—MATHEMATICAL REVIEWS
Booknews
For readers familiar with measure-theoretic probability and discrete time processes, who wish to explore stochastic processes in continuous time. Annotation c. Book News, Inc., Portland, OR (booknews.com)Product Details
Related Subjects
Table of Contents
Martingales, Stopping Times, and Filtrations.- Brownian Motion.- Shastic Integration.- Brownian Motion and Partial Differential Equations.- Shastic Differential Equations.- Lévy's Theory of Brownian Local Time.