Stochastic Processes (Courant Lecture Notes)

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. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

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

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