Brownian Motion and Stochastic Calculus

Graduate Texts in Mathematics #113

by Ioannis Karatzas

This book is designed for a graduate course in stochastic processes. It is written for the reader who is familiar with measure-theoretic probability and the theory of discrete-time processes who is now ready to explore continuous-time stochastic processes. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a Markov process and a martingale in continuous time. The authors show how, by means of stochastic integration and random time change, all continuous martingales and many continuous Markov processes can be represented in terms of Brownian motion. The text is complemented by a large number of exercises.

Genres: Mathematics, Finance, Reference, Textbooks

470 pages, Hardcover

First published January 1, 1987

Reviews

[smoh cat · Rating 3 out of 5]

Good reference book. However I can’t learn stochastic calculus from it as too many details were left unsaid. I was told this is easier compared to a similar French text.