Markov Processes, Winter semester 2026/27

Tuesdays 16.15-18.00 and Fridays 10.15-12.00, 1.008.

Lecture course: Andreas Eberle

Exercises: Piro Manco

Tutorial classes:

• Mondays 12-14, 1.008
• Tuesdays 14-16, 1.007

Exam: oral.

The course will give an applied introduction to Markov processes, convergence to equilibrium, and applications to sampling (Markov Chain Monte Carlo methods). It will mainly be based on the lecture notes

N. Bou-Rabee, A. Eberle: Markov Chain Monte Carlo methods

that are available on my homepage. Some parts will also be based on my lecture notes from last year

A. Eberle: Markov Processes, Lecture notes 2025/26

but the course will more closely follow the first lecture notes.

Topics to be covered include

• Markov chains, diffusion processes, processes with jumps, particle systems
• Markov Chain Monte Carlo methods
• Semigroups, generators, invariant probability measures
• Long time behaviour (ergodic theory, relaxation times and mixing times)
• Couplings and functional inequalities

In summer semester, another course on Markov Processes will be offered that develops more systematically the underlying mathematical theory. It is possible to take both courses if you bring in one of them as “Additional Advanced Topics”.

 

Further Material:

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Problem Sheets

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Simulations

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July 2026 Andreas Eberle eberle@uni-bonn.de