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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.



Dynamics of a Stochastic Excitable System with Slowly Adapting Feedback: Application to Izhikevich Neuronal Model
Tri Shrive


Applications of Optimal Control to the Dynamics of the Whole-Brain Network
Teresa Chouzouris
Frechet differentiable drift dependence of Perron-Frobenius and Koopman operators for SDEs
Han Cheng Lie

Optimal Control of stochastic
mean-field equations

Alexander Vogler

Katastrophische Filterdivergenz: Diskussion verschiedener Analysekriterien am Besipiel des ETKF
Jan-Henrik Paul
Stochastic filtering as an optimal control
problem: the feedback (particle) filter
Wilhelm Stannat

Large-scale Baysian linear regression with application to MR imaging
Jacopo  Zurbuch
An optimal transport formulation of the Ensemble Kalman Filter
Wilhelm Stannat
An optimal transport formulation of the Ensemble Kalman Filter, Part II
Wilhelm Stannat
Approximate McKean-Vlasov  representations for a class of SPDEs
Theresa Lange
Implicit equation-free methods applied
on noisy slow-fast systems
Anna Dittus
Backward SPDEs and random backward PDEs
Lukas Wessels


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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