Brownian motion : an introduction to stochastic processes

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. This text, tailored to the needs of graduate students, covers Brownian motion, its elementary properties, certain distributional aspects, path properties, as well as stochastic calculus based on Brownian motion and numerical simulation of Brownian motion. 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 arrange her/his own digest of material