Stochastic Processes and Applications (mod. 1)

Stochastic Processes
and Applications (mod. 1)

Credits

6

Prerequisites

None.

Examination method

Passing an integrated examination, possibly divided into several tests, on the contents of Stochastic Processes and Applications mod. 1 and Stochastic Processes and Applications mod. 2

Learning
objectives

In an initial phase, the fundamental contents of Probability Theory will be revisited with a more marked degree of formalism than in the basic courses. This serves both to consolidate and strengthen knowledge and to make the class more homogeneous. Subsequently, concepts, contents and tools forming the basis for an in-depth study of the theory of stochastic processes will be presented. A further objective is to enable students to grasp the relevant issues involved in constructing stochastic models used to describe certain classes of physical, biological and economic phenomena.

Contents

Conditional expectations. Stopping times. Martingales. Distribution of the maximum of discrete-time processes. Brownian motion. Some laws of Brownian motion. Analytical approach to Brownian motion. Applications.