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,  Jaime Díaz-Trechuelo Sánchez-Molini
• Tuesdays 14-16, N0.004 (PC-Pool),  Ilia Mirkis

Exam: oral.

Lecture Notes: Markov processes, mixing times and MCMC methods (in preparation)

The course will give an applied introduction to Markov processes, convergence to equilibrium, and applications to sampling (Markov Chain Monte Carlo methods). The lecture notes are composed of material from the following course notes from last year that are available on my homepage.

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

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

Topics to be covered include

• Markov chains and Markov processes in continuous time
• Semigroups, generators, invariant probability measures
• Markov Chain Monte Carlo methods
• 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

• Sheet 1 (due Monday 19.10.)

Simulations

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September 2026 Andreas Eberle eberle@uni-bonn.de