Stochastic Processes

Contents:

A 'stochastic process' is a random function X(t) where the value X(t) at an arbitrary 'time point' t is a random variable. Practical examples are provided by the level of a river at time t, the value of an asset, the grade of a disease, the location of a molecule (Brownian motion) etc.

The course presents an introduction into the mathematical theory of stochastic processes with an emphasis on the following types of processes:

Stationary processes
Wiener and Gauss processes, Brownian motion
Poisson process
Markov chains and Markov processes with continuous time
Martingales.

In addition, we develop some measure-theoretic tools and statistical methods for stochastic processes.

Prerequistes: Basic knowledge in probability and some measure thery.