Markov Processes

What it is about

You will learn theory and methods of continuous-time Markov processes: continuous-time Markov chains, the Markov property, Feller processes as well as properties of transition semigroups and their generators. In the end you can analyze the long-term behavior of processes, apply ergodic theorems and use them in examples (e.g. queueing theory, interacting particle systems, time series).

What you will be able to do

• Understand and apply the Markov property
• Carry out calculations with Q-matrices
• Determine invariant and reversible distributions
• Understand the basics of the theory of Feller processes
• Apply ergodic theorems
• Analyze the long-term behavior of given Markov processes

What the module consists of

• VorlesungPresentation of content, demonstration examples and discussion to convey the theory
• ÜbungAccompanying exercise sessions with problem sets and solutions for deepening and self-check

Teaching method

• VortragExplanation of content and motivation for one's own analysis
• DiskussionInteractive clarification of questions and deepening