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Seminar: Stochastische Partielle Differentialgleichungen
LV-Nr. 3236 L 365
Time: Mondays 14:15
Room: MA 748
Begin: October 14, 2019
The seminar offers perspectives on our current research in the area of stochastic models and partial differential equations. The seminar is particularly suitable for BSc and MSc students looking for a final project. Students, who want to obtain a "Seminarschein", are welcome as well.
Termine
| Date | Title | Speaker | Advisor |
|---|---|---|---|
| 21.10. | Dynamics of a Stochastic Excitable System with Slowly Adapting Feedback: Application to Izhikevich Neuronal Model | Tri Shrive | |
| 28.10. | |||
| 4.11. | |||
| 11.11. | Applications of Optimal Control to the Dynamics of the Whole-Brain Network | Teresa Chouzouris | |
| 18.11. | Frechet differentiable drift dependence of Perron-Frobenius and Koopman operators for SDEs | Han Cheng Lie | |
| 25.11. | Optimal Control of stochastic mean-field equations | Alexander Vogler | |
| 02.12. | Katastrophische Filterdivergenz: Diskussion verschiedener Analysekriterien am Besipiel des ETKF | Jan-Henrik Paul | |
| 09.12. | Stochastic filtering as an optimal control problem: the feedback (particle) filter | Wilhelm Stannat | |
| 16.12. | |||
| 06.01. | Large-scale Baysian linear regression with application to MR imaging | Jacopo Zurbuch | |
| 13.01. | An optimal transport formulation of the Ensemble Kalman Filter | Wilhelm Stannat | |
| 20.01. | An optimal transport formulation of the Ensemble Kalman Filter, Part II | Wilhelm Stannat | |
| 27.01 | Approximate McKean-Vlasov representations for a class of SPDEs | Theresa Lange | |
| 03.02. | Implicit equation-free methods applied on noisy slow-fast systems | Anna Dittus | |
| 10.02. | Backward SPDEs and random backward PDEs | Lukas Wessels |
Literatur
Stochastic Filtering, Data Assimilation:
[F1] B. Fristedt, N, Jain and N. Krylov: Filtering and Prediction: A Primer, Student Mathematical Library, Vol. 38, AMS, 2007
[F2] K. J. H. Law, A. M. Stuart, K. C. Zygalakis: “Data assimilation: a mathematical introduction” homepages.warwick.ac.uk/~masdr/data_assimilation/book_excerpt.pdf
[F3] T. Karvonen: “Stability of linear and non-linear Kalman filters” Master’s thesis users.aalto.fi/~karvont2/
[F4] S. P. Meyn, R. L. Tweedie “Markov chains and stochastic stability”
[F5] Dembo/Zeitouni – Parameter Estimation of Partially Observed Continuous Time Stochastic Processes via the EM algorithm
James/LeGland – Consistent Parameter Estimation for Partially Observed Diffusions with Small Noise https://www.sciencedirect.com/science/article/pii/0304414986900189
https://link.springer.com/content/pdf/10.1007/BF01189903.pdf
[F6] Kalman 1960: A New Approach to Linear Filtering and Prediction Problems; Kalman, Bucy 1961: New Results in Linear Filtering and Prediction Theory www.cs.unc.edu/~welch/kalman/media/pdf/Kalman1960.pdf
[F7] Wonham: On the Separation Theorem of Stochastic Control; Fleming, Rishel: Deterministic and Stochastic Control, Springer 1975: Kapitel 6, Abschnitt 11 epubs.siam.org/doi/pdf/10.1137/0306023
Stochastic Control:
[O1] T. Breiten, K. Kunisch, L. Pfeiffer: Control Strategies for the Fokker-Planck Equation arxiv.org/abs/1707.07510
[O2] L. Pfeiffer: Numerical Methods for Mean-Field-Type Optimal Control Problems, Pure Appl. Funct. Anal. 1 (2016), no. 4, 629–655. arxiv.org/abs/1703.10001
[O3] L. Pfeiffer: Optimality conditions for mean-field type optimal control problems, TU Graz, SFB-Report-2015-015 https://imsc.uni-graz.at/mobis/publications/SFB-Report-2015-015.pdf
[O4] L. Pfeiffer: Two approaches to stochastic optimal control problems with a final-time expectation constraint. Appl. Math. Optim. 77 (2018), no. 2, 377–404. link.springer.com/article/10.1007/s00245-016-9378-9