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TU Berlin

Inhalt des Dokuments

Prof. Dr. Wilhelm Stannat

Submitted/in preparation
with S. Ertel, Analysis of the Ensemble Kalman--Bucy Filter for correlated observation noise, arXiv:2205.14235
with L. Wessels, Necessary and Sufficient Conditions for Optimal Control of Semilinear Stochastic Partial Differential Equations, arXiv:2112.09639.
with F. Seib, J. Tölle, Stability and moment estimates for the stochastic singular Phi-Laplace equation, arXiv:2103.03194.
Accepted for publication
with H. Lee, G. Trutnau, Analytic theory of Itô-stochastic differential equations with non-smooth coefficients, arxiv:2012.14410, to appear as SpringerBriefs in Probability and Mathematical Statistics, 2022.  

Publications (refereed)
with S. Pathiraja, Analysis of the feedback particle filter with diffusion map based approximation of the gain, Foundations of Data Science, Vol 3, 615-645, 2021.
with S. Pathiraja, S. Reich, McKean-Vlasov SDEs in nonlinear filtering,
SIAM J. Control Optim., Vol 59, 
4188–4215, 2021
with L. Wessels, Peng's Maximum Principle for Stochastic Partial Differential Equations, SIAM J. Control Optim., Vol 59, 3552-3573, 2021
with S. Heesen, Fluctuation limits for mean-field interacting nonlinear 
Hawkes processes, Stochastic Process. Appl., Vol 139, 280-297, 2021
with T. Lange, On the continuous time limit of Ensemble Square Root Filters, Commun. Math. Sci., Vol 19, 1855-1880, 2021.
with G. Pasemann, S. Flemming, S. Alonso, C. Beta, Diffusivity estimation for Activator-Inhibitor Models: theory and application to intracellular dynamics of the actin cytoskeleton, Journal of Nonlinear Science, Vol 31, Article number 59, 2021
with T. Lange, Mean field limit of Ensemble Square Root Filters - discrete and continuous time, Foundations of Data Science, Vol 3, 563-588, 2021.
with T. Lange, On the continuous time limit of the Ensemble Kalman Filter, Math. Comp., Vol 90, 233–265, 2021.
with L. Wessels, Deterministic Control of Stochastic Reaction-Diffusion Equations, Evolution Equations and Control Theory, Vol 10, 701-722, 2021
with S. Mehri, M. Scheutzow, B. Zangeneh, Propagation of Chaos for Stochastic Spatially Structured Neuronal Networks with Delay driven by Jump Diffusions, Ann. Appl. Probab., Vol. 30, 175-207, 2020.
with G. Pasemann, Drift Estimation for Stochastic Reaction-Diffusion Systems, accepted for publication in Electronic Journal of Statistics,  Electron. J. Stat., Vol 14, 547-579, 2020.

with P. Friz, T. Nilssen, Existence, uniqueness and stability of semi-linear rough partial differential equations, J. Differential Equations, Vol. 268, Issue 4, 1686-1721, 2020.
with A. Hocquet, T. Nilssen, Generalized Burgers equation with rough transport noise, Stochastic Proc. Appl., Vol. 130, Issue 4, 2159-2184 2019.
with S. Mehri, Weak Solutions to Vlasov-McKean Equations under Lyapunov type conditions, Stoch. Dyn., Vol. 19, No. 06, 1950042, 2019.
with Y. Shen, V. Laschos, K. Obermayer, A Fenchel-Moreau-Rockafellar type theorem on the Kantorovich-Wasserstein space with Application in Partially Observable Markov Decision Processes, J. Math. Anal. Appl., Vol. 477, 1133–1156, 2019.
with Y. Chen, R. M. Cichy, J.-D. Haynes, Scale-specific analysis of fMRI data on the irregular cortical surface, NeuroImage 181, Vol. 181, 370-381, 2018.
Eberle, A., Grothaus, M., Hoh, W., Kassmann, M., Stannat, W., Trutnau, G. (Eds.), Stochastic Partial Differential Equations and Related Fields. In Honor of Michael Röckner SPDERF, Bielefeld, Germany, October 10 -14, 2016, Springer Proceedings in Mathematics & Statistics, 2018. 
with J. de Wiljes, S. Reich, Long-time stability and accuracy of the ensemble Kalman-Bucy filter for fully observed processes and small measurement noise, SIAM J. Appl. Dyn. Syst., Vol. 17, 1152-1181,

with J. Diehl, P. Friz, Stochastic partial differential equations: a rough path view on weak solutions via Feynman-Kac, Annales de la Faculte des Sciences de Toulouse Ser. 6, Vol. XXVI, 911-947, 2017.
with F. Farkhooi, A complete mean-field theory for dynamics of binary recurrent neural networks, Phys. Rev. Lett. 119, 208301, 2017.
with J. Krüger, Well-posedness of the stochastic neural field equation with discontinuous firing rate, Journal of Evolution Equations 2017.
with J. Krüger, A Multiscale-Analysis of Stochastic Bistable Reaction-Diffusion Equations, Nonlinear Analysis, Vol. 162, 197--223, 2017.

with E. Lang, Finite-Size Effects on Traveling Wave Solutions to Neural Field Equations, The Journal of Mathematical Neuroscience, 2017, 7:5
with E. Lucon, Transition from Gaussian to non-Gaussian fluctuations for mean-field diffusions in spatial interaction, Ann. Appl. Probab., Vol. 26, 3840-3909, 2016.

with E. Lang, L2-Stability of Traveling Wave Solutions to Nonlocal Evolution Equations, J. Differential Equations, Vol. 261, pp. 4275-4297, 2016

with M. Sauer, Reliability of signal transmission in stochastic nerve axon equations, Journal of Computational Neuroscience, Vol. 40, pp. 103-111,2016.
with M. Sauer, Analysis and Approximation of Stochastic Nerve Axon Equations, Math. Comp., Vol. 85, 2457-2481, 2016.

with Y. Shen, K. Obermayer, A Unified Framework for Risk-sensitive Markov Control Processes, IEEE 53rd Annual Conference on Decision and Control (CDC), 2014.
with S. Voronenko, B. Lindner,Shifting spike times or adding and deleting spikes - how different types of noise shape signal transmission in neural populations, The Journal of Mathematical Neuroscience, 2015, 5:1
with S. Yokoyama, Weak solutions of non-coercive stochastic Navier-Stokes equations in R2, Aust. J. Math. Anal. Appl., Vol. 11, Article 17, pp. 1-19, 2014.
with J. Diehl, P. Friz, H. Mai, H. Oberhauser, S. Riedel, Robustness in stochastic filtering and maximum likelihood estimation for SDEs, in:
Extraction of Quantifiable Information from Complex Systems, Editors: S. Dahlke, et al., Lecture Notes in Computational Science and Engineering, Vol. 102, Springer, 161-178, 2014.
with J. Krüger, Front Propagation in Stochastic Neural Fields: A rigorous mathematical framework, SIAM J. Appl. Dyn. Syst., Vol. 13, 1293–1310, 2014. 
with M. Sauer, Lattice Approximation for Stochastic Reaction Diffusion Equations with One-sided Lipschitz Condition, Math. Comp. Vol. 84,  743-766, 2015
with E. Lucon, Mean Field Limit for disordered diffusions with singular interactions, Ann. Appl. Probab., Vol. 24, 1946-1993, 2014.
with Y. Shen, K. Obermayer, Risk-sensitive Markov Control Processes,  SIAM J. Control Optim., Vol. 51, 3652-3672, 2013.
Two Remarks concerning the Wasserstein Dirichlet form, Random Fields and Applications VII, Ascona, May 2011, Editors: R. Dalang et al., Progress in Probability, Vol. 67, Birkhäuser, 235-255, 2013.
with M. Hieber, Stochastic Stability of the Ekman Spiral, manuscript, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5), Vol. 12, 189-208, 2013.
with A. Es-Sarhir, M.-K. von Renesse, Estimates for the ergodic measure and polynomial stability of plane stochastic curve shortening flow, NoDEA vol. 19, 663-675, 2012.

Stochastic partial differential equations: Kolmogorov operators and invariant measures, Jahresbericht der deutschen Mathematiker-Vereinigung, Vol. 113, 81-109, 2011.  
Lp-Uniqueness of Kolmogorov operator associated with 2D-Stochastic Navier-Stokes -Coriolis equations, Mathematische Nachrichten, vol 284, 2287-2296, 2011.  
with A. Es-Sarhir, Improved moment estimates for invariant measures of semilinear diffusions in Hilbert spaces and application, J. Funct. Anal.  Vol. 259, 1248–1272, 2010.  
Stability of the optimal filter for nonergodic signals - a variational approach, in: The Oxford Handbook on Nonlinear Filtering, Eds.: D. Crisan, B. Rozovskii, Oxford University Press, Oxford, 374-399, 2011.   
Functional Inequalities for the Wasserstein Dirichlet Form. In: Seminar on Stochastic Analysis, Random Fields and Applications VI, Ascona, May 2008, Editors: R. Dalang et al., Progress in Probability, Vol. 63, Birkhäuser, 245-260, 2011.
with A. Es-Sarhir, Maximal Dissipativity of Kolmogorov operators with Cahn-Hilliard type Drift term, Journal of Differential Equations, Vol. 247, Issue 2, 424-446, 2009.   
with M. Döring, The Logarithmic Sobolev inequality for the Wasserstein diffusion, Probab. Theory Relat. Fields, Vol. 145, 189-209, 2009. 
Lipschitz continuity of the pseudo resolvent of the stochastic Burgers equation. In: Potential Theory and Stochastics in Albac, Albac 2007, Editors: D. Bakry, et al., Theta Series in Advanced Mathematics, Theta, 225-237, 2009.
A new a priori estimate for the Kolmogorov operator of a 2D-stochastic Navier-Stokes equation, Infin. Dimens. Anal. Quantum Probab. Relat. Top., Vol. 10, Issue 4, 483-497, 2007.
with A. Es-Sarhir, Invariant measures for Semilinear SPDE's with local Lipschitz Drift Coefficients and applications, Journal of Evolution Equations, Vol. 8, No. 1, 129-154, 2008.  
with V.I. Bogachev, G. Da Prato, M. Röckner, Uniqueness of solutions to weak parabolic equations for measures, Bull. London Math. Soc., Vol. 39, Part 4, 631-640, 2007.
On the stability of Feynman-Kac propagators. In: Stochastic Analysis, Ascona 2005, Editors: R. Dalang et al., Progress in Probability, Vol. 59, Birkhäuser, 345-362, 2007.
Stability of the optimal filter via pointwise gradient estimates. In: Stochastic Partial Differential Equations and Applications VII, Editors: G. da Prato et al., Lecture Notes in Pure and Applied Mathematics, CRC Press, Taylor & Francis Group , Boca Raton, 281-293, 2005.
Stability of the pathwise filter equation for a time-dependent signal on Rd, in Appl.  Math. Optim., Vol. 52, No. 1, 39-71, 2005.
On the Poincare inequality for infinitely divisible measures, Potential Analysis, Vol. 23, No. 3, 279 - 301, 2005.
Time-Dependent Diffusion operators on L1, Journal of Evolution Equations, Vol. 4, No. 4, 463-495, 2004.
A remark on the CLT for a random walk in a random environment, Probab. Theory Relat. Fields, Vol. 130, No. 3, 377-387, 2004.
On the convergence of genetic algorithms - a variational approach, Probab. Theory Relat. Fields, Vol. 129, No.1, 113-132, 2004.
Spectral Properties for a class of continuous state branching processes with immigration, J. Funct. Anal., Vol. 201, No. 1, 185-227, 2003.
On transition semigroups of (A ,Psi)- superprocesses with immigration, Ann. Probab., Vol. 31, No. 3, 1377-1412, 2003.
L1-Uniqueness of regularized 2D-Euler and Stochastic Navier-Stokes Equations, J. Funct. Anal., Vol. 200, No.1,  101-117, 2003.
with V.I. Bogachev, M. Röckner: Uniqueness of solutions for elliptic equations and uniqueness of invariant measures of diffusions. Mat. Sb., Vol. 193, No. 7, 3-36. English translation in Sb. Math., Vol. 193, No. 7, 945-976, 2002.
Long-time behaviour and regularity properties of transition semigroups of Fleming-Viot processes, Probab. Theory Relat. Fields, Vol. 122, 431-469, 2002.
with V.I. Bogachev, M. Röckner, Uniqueness of Invariant Measures and Maximal Dissipativity of Diffusion Operators on L1, in: Infinite dimensional stochastic analysis, Editors: P. Clement et al. Amsterdam, Royal Netherlands Academy of Arts and Sciences, 39-54, 2000.
On the Validity of the Log-Sobolev inequality for symmetric Fleming-Viot operators. Ann. Probab., Vol. 28, No. 2, 667-684, 2000.
(Nonsymmetric) Dirichlet Operators on L1: Existence, Uniqueness and associated Markov Processes. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), Vol. 28, No. 1, 99-140, 1999.
The Theory of Generalized Dirichlet Forms and Its Applications in Analysis and Stochastics, Dissertation, Bielefeld 1996. Published as Memoirs of the AMS, Vol. 142, No. 678, 1999.
Dirichlet Forms and Markov Processes: A Generalized Framework including both Elliptic and Parabolic Cases, Potential Analysis, Vol. 8, No. 1, 21-60, 1998.
First Order Perturbations of Dirichlet Operators: Existence and Uniqueness, J. Funct. Anal., Vol. 141, No. 1, 216-248, 1996.
with S. Albeverio, R.Z. Fan, M. Röckner, A Remark on Coercive Forms and Associated Semigroups, in: Partial differential operators and Mathematical physics. Operator Theory Advances and Applications, Vol. 78, 1-8, Basel: Birkhäuser 1995.
Generalized Dirichlet forms and associated Markov processes, C. R. Acad. Sci. Paris, t. 319, 1063-1068, 1994.
C.L. Epstein, R. Mazzeo, ''Degenerate Diffusion Operators Arising in Population Biology'', Jahresber Dtsch Math-Ver, 2015.
Ausgewählte Abstracts
Statistical problems in nerve axon equations. In: Computational Inverse Problems for Partial Differential Equations, Editors, L. Borcea, et al., Oberwolfach Reports, Vol. 14, Issue 2, 1463--1549, 2017.

Stochastic nerve axon equations. In: Dirichlet forms and its applications, Editors: S. Albeverio, et al., Oberwolfach Reports, Vol. 11, 2667--2756, 2014.
Stochastic partial differential equations in mathematical fluid dynamics. In: Geophysical Fluid Dynamics, Editors: Y. Giga, et al., Oberwolfach Reports, Vol. 10, 483–520, 2013. 
Stability of the optimal filter - a variational approach. In: Mathematical and Algorithmic Aspects of Atmosphere-Ocean Data Assimilation, Editors: A. Griewank, et al., Oberwolfach Reports, Vol. 9, 3417–3471, 2012.
On stability of the optimal filter for nonergodic signals. In: Mathematical Population Genetics, Editors: E. Baake, et al., Oberwolfach Reports, Vol. 2, Issue 3, 2241-2304, 2005.
Arbeiten in den Ingenieurwissenschaften 
Maintaining Replicas in Unstructured Peer-to-Peer Systems (with C. Lang, W. Terpstra, B. Kemme, A.P. Buchmann) Proceedings of 2008 ACM CoNEXT Conference.
Unveröffentlichte Preprints
with Y. Shen, K. Obermayer, Risk-sensitive Markov Control Processes with strictly convex risk maps, arXiv:1403.3321.
Stability of travelling waves in stochastic bistable reaction diffusion equations, arXiv:1404.3853.
Stability of travelling waves in stochastic Nagumo equations, preprint arXiv:1301.6378.
Analysis of Measure-Valued Processes and Infinite Dimensional Differential Operators, Habilitationsschrift, U Bielefeld 2002.
The Theory of Generalized Dirichlet Forms and Its Applications in Analysis and Stochastics, Dissertation, U Bielefeld 1996.
Verallgemeinerte zeitabhängige Dirichletformen, Diplomarbeit, U Bonn 1993. 

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