241016 Fokker-Planck equations (VÜA) (SoSe 2024)
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.
Requirements for participation, required level
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Notwendig: Measure theory, functional analysis, probability theory (Brownian motion, Markov processes); Empfohlen: Basic stochastic analysis (Itô-formula, martingales, SDEs, martingale problem) and PDE theory
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
Dates ( Calendar view )
| Frequency | Weekday | Time | Format / Place | Period | |
|---|---|---|---|---|---|
| weekly | Mo | 8-10 | E01-108 | 08.04.-19.07.2024
not on: 5/20/24 |
Übung |
| weekly | Mi | 8-10 | E01-108 | 08.04.-19.07.2024
not on: 5/1/24 |
Vorlesung |
Subject assignments
| Module | Course | Requirements | |
|---|---|---|---|
| 24-M-P1 Profilierung 1 | Profilierungsvorlesung (mit Übung) - Typ 3 | Study requirement
|
Student information |
| 24-M-P1a Profilierung 1 Teil A | Profilierungsvorlesung (mit Übung) - Typ 3 | Study requirement
|
Student information |
| 24-M-P1b Profilierung 1 Teil B | Profilierungsvorlesung (mit Übung) - Typ 3 | Student information | |
| 24-M-P2 Profilierung 2 | Profilierungsvorlesung (mit Übungen) - Typ 3 | Study requirement
|
Student information |
| 24-M-PWM Profilierung Wirtschaftsmathematik | Profilierungsvorlesung (mit Übung) -Typ 3 | Study requirement
|
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.
| Degree programme/academic programme | Validity | Variant | Subdivision | Status | Semester | LP | |
|---|---|---|---|---|---|---|---|
| Bielefeld Graduate School in Theoretical Sciences / Promotion | |||||||
| Mathematik / Promotion | Subject-specific qualification | 2 | aktive Teilnahme |
- Registered number: 12
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- Last update basic details/teaching staff:
- Monday, December 11, 2023
- Last update times:
- Tuesday, February 13, 2024
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- Tuesday, February 13, 2024
- Type(s) / SWS (hours per week per semester)
- VÜA / 3
- Language
- This lecture is taught in english
- Department
- Faculty of Mathematics
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