Stochastic ProcessesShare this page
S. R. S. Varadhan
A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University
This is a brief introduction to stochastic processes studying certain
elementary continuous-time processes. After a description
of the Poisson process and related processes with independent increments
as well as a brief look at Markov processes with a
finite number of jumps, the author proceeds to introduce Brownian motion
and to develop stochastic integrals and Itô's theory in the
context of one-dimensional diffusion processes. The book ends with a
brief survey of the general theory of Markov processes.
The book is based on courses given by the author at the Courant Institute and can be used as a sequel to the author's successful book Probability Theory in this series.
Srinivasa S. R. Varadhan is the winner of the 2007 Abel Prize. Varadhan was awarded the prize "for his fundamental contributions to probability theory and in particular for creating a unified theory of large deviations". Read more here.
Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.
Table of Contents
Table of Contents
Graduate students and research mathematicians interested in stochastic processes.
The text is one of those that may be strongly recommended to all young mathematicians as a starter to precede a deeper study of probability and stochastic processes.
-- EMS Newsletter
Amazingly, almost all of the proofs are given explicitly. In fact the author provides only eight references in the bibliography. This reflects the fact that, as a whole, this book is written in a totally self-contained manner. ...I can say that this book is a set of very well-written lecture notes, and it is organized as a clear synthesis of the theory of continuous-time stochastic processes with many examples and with plenty of exercises...
-- Mathematical Reviews