240193 Linear and nonlinear Fokker—Planck equations (VÜA) (WiSe 2026/2027)
Contents, comment
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Fokker--Planck equations (FPE) are differential equations for measures. We will reveal the central role FPEs play as a bridge between stochastics and analysis. In itself, they are an interesting class of equations with close connections to PDEs. The most striking aspect, which has sparked substantial recent research interest, is the intimate connection to stochastic analysis: Every stochastic differential equation has a FPE such that the one-dimensional time marginals of solutions of the former solve the latter. After an introduction to the topic, our first cornerstone will be the superposition principle, which reverses this relation. We shall also study the connection to Markov processes.
Bibliography
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V. Bogachev, N. Krylov, M. Röckner, S. Shaposhnikov: Fokker-Planck-Kolmogorov equations; D. Stroock, S. Varadhan: Multidimensional Diffusion Processes; D. Trevisan: Well-posedness of Multidimensional Diffusion Processes with Weakly Differentiable Coefficients.
Teaching staff
- Dr. Marco Rehmeier
Dates ( Calendar view )
| Frequency | Weekday | Time | Format / Place | Period | |
|---|---|---|---|---|---|
| weekly | Mi | 12-14 | U2-205 | 12.10.2026-05.02.2027 | Lecture |
| weekly | Fr | 12-14 | V4-116 | 12.10.2026-05.02.2027 | Tutorium |
Subject assignments
| Module | Course | Requirements | |
|---|---|---|---|
| 24-M-AN-ST5a Selected Topics in Analysis 1 | Lecture Selected Topics in Analysis | Graded examination
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| Tutorials Selected Topics in Analysis | Study requirement
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| 24-M-AN-ST5b Selected Topics in Analysis 2 | Lecture Selected Topics in Analysis | Graded examination
|
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| Tutorials Selected Topics in Analysis | Study requirement
|
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| 24-M-P1 Profile Module 1 | Profilierungsvorlesung (mit Übung) - Typ 2 | Study requirement
|
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| 24-M-P1a Profile Module 1, Part A | Profilierungsvorlesung (mit Übung) - Typ 2 | Study requirement
|
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| 24-M-P1b Profile Module 1, Part B | Profilierungsvorlesung (mit Übung) - Typ 2 | Study requirement
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| 24-M-P2 Profile Module 2 | Profilierungsvorlesung (mit Übungen) - Typ 2 | Study requirement
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| 24-M-PWM Profile Module Economic Mathematics | Profilierungsvorlesung (mit Übung) -Typ 2 | Study requirement
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Student information |
The binding module descriptions contain further information, including specifications on the "types of assignments" students need to complete. In cases where a module description mentions more than one kind of assignment, the respective member of the teaching staff will decide which task(s) they assign the students.
Notwendig: Measure theory, functional analysis, probability theory (Brownian motion, Markov processes); Empfohlen: Basic stochastic analysis (Itô-formula, martingales, SDEs, martingale problem) and PDE theory
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- Friday, August 21, 2026
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- Tuesday, August 25, 2026
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- Tuesday, August 25, 2026
- Type(s) / SWS (hours per week per semester)
- lecture with exercises (VÜA) / 4
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- This lecture is taught in english
- Department
- Faculty of Mathematics
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