Bücher

Brownian Motion and Stochastic CalculusIoannis Karatzas Art Nr.: 0387976558 ISBN 13: 9780387976556 Release year: 2004 Published by: Springer New York Edition: Taschenbuch Cover: Taschenbuch Cover Format: 235x155x26 mm Pages: 496 Weight: 744 g Language: Englisch Author: Ioannis Karatzas Description 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. Powered by INFORIUS