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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.
20.01.

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”

probability.ca/MT/BOOK.pdf

[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

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