Faculty of Science

Objectives

To introduce the notions of stochastic integration with respect to the Wiener process, stochastic differentials and stochastic differential equations. The ideas introduced here are central in modern stochastic analysis, mathematical finance, and statistics of stochastic processes.

Contents

Brownian motion in one and several dimensions; Construction of Brownian motion; Wiener measure; Markov properties of Brownian motion; Properties of Brownian sample paths; Stochastic integrals with respect to Brownian Motion; Definition and elementary properties of the integral; Stratonovich and Ito integrals – relations; Ito Formula;appreciation of the Ito formula; stochastic differentials and stochastic differential equations; Existence and uniqueness of strong and weak solutions of stochastic differential equations; Markov properties of solutions of stochastic differential equations; Generators and Diffusions – Dynkin’s Formula.