Stochastic Processes (Courant Lecture Notes in Mathematics)

the long version

"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 Ito'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."--Jacket.