Stochastic Processes - Einzelansicht

Stochastic processes play a central role in many scientific areas.

This lecture is thought as an introduction to the theory of Markov chains, in discrete time and continuous time.

• R. Durett, Essentials of stochastic processes, 1999
• N. Norris, Markov Chains, 1998
• N. Privault, Understanding Markov Chains: Examples and Applications, 2018

The course is a natural application / extension of the course Aufbaumodul Stochastik.

Prerequisite: Course "Stochastics" or "Foundations of stochastics", optimal "Advanced Probability Theory"

Written Exam

Important concepts concerning Markov Chains with discrete time and discrete state space:

- recurrence and transience,

- stationary and reversible distributions,

- first-passage-time methods,

- convergence towards the stationary distribution.

A number of examples are analyzed, in particular models from physics (random walk) or from biology (branching processes).

This lecture is appropriate for Master students in Mathematics and/or in Data Science, and for advanced Bachelor students.

It is part of both profiles "Mathematical modeling and data analysis" and "Structures of Mathematics with physical background" in the course of studies Master of Science Mathematics.

The lecture also addresses to students of Master of Data Science, informatics and physics.