Stochastic processes occur in a large number of fields in sciences and engineering, so they need to be understood by applied mathematicians, engineers and scientists alike. This work is ideal for a first course introducing the reader gently to the subject matter of stochastic processes. It uses Brownian motion since this is a stochastic process which is central to many applications and which allows for a treatment without too many technicalities. All chapters are modular and are written in a style where the lecturer can "pick and mix" topics. A "dependence chart" will guide the reader when...

This volume presents the lecture notes from two courses given by Davar Khoshnevisan and Rene Schilling, respectively, at the second Barcelona Summer School on Stochastic Analysis.

Rene Schilling s notes are an expanded version of his course on Levy and Levy-type processes, the purpose of which is two-fold: on the one hand, the course presents in detail selected properties of the Levy processes, mainly as Markov processes, and their different constructions, eventually leading to the celebrated Levy-Ito decomposition. On the other, it identifies the infinitesimal generator of the Levy...