Inhalt des Dokuments
Seminar: Stochastische Partielle Differentialgleichungen
LV-Nr. 3236 L 365
Prof. Dr. Wilhelm Stannat [1]
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 [2]
[F3] T. Karvonen: “Stability of linear and non-linear Kalman filters” Master’s thesis users.aalto.fi/~karvont2/ [3]
[F4] S. P. Meyn, R. L. Tweedie “Markov chains and stochastic stability”
probability.ca/MT/BOOK.pdf [4]
[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
[5]
https://link.springer.com/content/pdf/10.1007/BF01189903.pdf
[6]
[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 [7]
[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 [8]
Stochastic Control:
[O1] T. Breiten, K. Kunisch, L. Pfeiffer: Control Strategies for the Fokker-Planck Equation arxiv.org/abs/1707.07510 [9]
[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 [10]
[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 [11]
[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 [12]
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tion/book_excerpt.pdf
304414986900189
89903.pdf
an1960.pdf
port-2015-015.pdf
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