Diffusions, Markov Processes and Martingales: Volume 2, Itô Calculus

Cambridge Mathematical Library

by L.C.G. Rogers, David Williams

The second volume concentrates on stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes. These subjects are made accessible in the many concrete examples that illustrate techniques of calculation, and in the treatment of all topics from the ground up, starting from simple cases. Many of the examples and proofs are new; some important calculational techniques appear for the first time in this book.

Genres: Mathematics

496 pages, Paperback

First published December 1, 1987

Reviews

[Christian Chapman · Rating 4 out of 5]

These objects require a lot of care to correctly describe in full generality. This book and Volume I served as my first exposure to the theory. I read through them and did some of the exercises, though stopped following the proofs in the middle of Volume II. I suppose the volumes are as gentle as they can be for how dense they are. They cannot be called an easy read. It would take years to achieve fluency in all the material covered.

In principle, everything needed to develop a working understanding of stochastic calculus is conveniently presented. "The list of algebra rules" that Ito/Stratonovich integrals follow under certain regularity conditions are each collected in one listing. Each idea gets its own several-pages section.

However, there is so much ground to cover that there is only room for examples of either fundamental importance (e.g. relations across/between Brownian motion and Bessel processes) or extremes that demonstrate need for a general theory.

To do anything practical involving stochastic calculus I would (or will) need to look things up online or find a higher level book/slide deck. I cannot remember, for example, which filtration each theorem towards the end requires. I cannot say I followed everything but the topic is less mysterious to me now thanks to these books.

[Richard Marney · Rating 4 out of 5]

I covered selected chapters only. For those in the field, a useful text.

[Daniel · Rating 4 out of 5]

Good, comprehensive whilst not being unnecessarily formal.