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Inhalt des Dokuments

Prof. Dr. Wilhelm Stannat

Submitted/In Preparation
with L. Wessels, Necessary and Sufficient Conditions for Optimal Control of Semilinear Stochastic Partial Differential Equations, arXiv:2112.09639 [1], submitted.
with F. Seib, J. Tölle, Stability and moment estimates for the stochastic singular Phi-Laplace equation, arXiv:2103.03194 [2] , submitted.
Accepted for publication
with H. Lee, G. Trutnau, Analytic theory of Itô-stochastic differential equations with non-smooth coefficients, arxiv:2012.14410 [3], to appear as SpringerBriefs in Probability and Mathematical Statistics, 2022.   [4]

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. [5]
with S. Pathiraja, S. Reich, McKean-Vlasov SDEs in nonlinear filtering,
SIAM J. Control Optim., Vol 59,  [6]
4188–4215, 2021 [7]. 
with L. Wessels, Peng's Maximum Principle for Stochastic Partial Differential Equations, SIAM J. Control Optim., Vol 59, 3552-3573, 2021 [8]. 
with S. Heesen, Fluctuation limits for mean-field interacting nonlinear 
Hawkes processes, Stochastic Process. Appl., Vol 139, 280-297, 2021 [9]. 
with T. Lange, On the continuous time limit of Ensemble Square Root Filters, Commun. Math. Sci., Vol 19, 1855-1880, 2021 [10].
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 [11]. 
with T. Lange, Mean field limit of Ensemble Square Root Filters - discrete and continuous time, Foundations of Data Science, Vol 3, 563-588, 2021 [12].
with T. Lange, On the continuous time limit of the Ensemble Kalman Filter, Math. Comp., Vol 90, 233–265, 2021 [13].
with L. Wessels, Deterministic Control of Stochastic Reaction-Diffusion Equations, Evolution Equations and Control Theory, Vol 10, 701-722, 2021 [14]. 
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 [15].
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. [17]
with A. Hocquet, T. Nilssen, Generalized Burgers equation with rough transport noise, Stochastic Proc. Appl., Vol. 130, Issue 4, 2159-2184 2019. [18]
with S. Mehri, Weak Solutions to Vlasov-McKean Equations under Lyapunov type conditions, Stoch. Dyn., Vol. 19, No. 06, 1950042, 2019. [19]
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. [20]
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. [21]
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.  [22]
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,
2018. [23]
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. [24]
with F. Farkhooi, A complete mean-field theory for dynamics of binary recurrent neural networks, Phys. Rev. Lett. 119, 208301, 2017 [25].
with J. Krüger, Well-posedness of the stochastic neural field equation with discontinuous firing rate, Journal of Evolution Equations 2017 [26].
with J. Krüger, A Multiscale-Analysis of Stochastic Bistable Reaction-Diffusion Equations, Nonlinear Analysis, Vol. 162, 197--223, 2017 [27].

with E. Lang, Finite-Size Effects on Traveling Wave Solutions to Neural Field Equations, The Journal of Mathematical Neuroscience, 2017, 7:5 [28]
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 [29].

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. [31]
with M. Sauer, Analysis and Approximation of Stochastic Nerve Axon Equations, Math. Comp., Vol. 85, 2457-2481, 2016. [32]

with Y. Shen, K. Obermayer, A Unified Framework for Risk-sensitive Markov Control Processes, IEEE 53rd Annual Conference on Decision and Control (CDC), 2014. [33]
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 [34]
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. [35]
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. [36]
with J. Krüger, Front Propagation in Stochastic Neural Fields: A rigorous mathematical framework, SIAM J. Appl. Dyn. Syst., Vol. 13, 1293–1310, 2014. [37] 
with M. Sauer, Lattice Approximation for Stochastic Reaction Diffusion Equations with One-sided Lipschitz Condition, Math. Comp. Vol. 84,  743-766, 2015 [38]
with E. Lucon, Mean Field Limit for disordered diffusions with singular interactions, Ann. Appl. Probab., Vol. 24, 1946-1993, 2014. [39]
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. [40]
with M. Hieber, Stochastic Stability of the Ekman Spiral, manuscript, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5), Vol. 12, 189-208, 2013. [41]
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. [42]
Stochastic partial differential equations: Kolmogorov operators and invariant measures, Jahresbericht der deutschen Mathematiker-Vereinigung, Vol. 113, 81-109, 2011.   [44]
Lp-Uniqueness of Kolmogorov operator associated with 2D-Stochastic Navier-Stokes -Coriolis equations, Mathematische Nachrichten, vol 284, 2287-2296, 2011.   [45]
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.   [46]
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.    [47]
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. [48]
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.    [49]
with M. Döring, The Logarithmic Sobolev inequality for the Wasserstein diffusion, Probab. Theory Relat. Fields, Vol. 145, 189-209, 2009.  [50]
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. [51]
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. [52]
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.   [53]
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. [54]
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. [55]
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. [56]
Stability of the pathwise filter equation for a time-dependent signal on Rd, in Appl.  Math. Optim., Vol. 52, No. 1, 39-71, 2005. [57]
On the Poincare inequality for infinitely divisible measures, Potential Analysis, Vol. 23, No. 3, 279 - 301, 2005. [58]
Time-Dependent Diffusion operators on L1, Journal of Evolution Equations, Vol. 4, No. 4, 463-495, 2004. [59]
A remark on the CLT for a random walk in a random environment, Probab. Theory Relat. Fields, Vol. 130, No. 3, 377-387, 2004. [60]
On the convergence of genetic algorithms - a variational approach, Probab. Theory Relat. Fields, Vol. 129, No.1, 113-132, 2004. [61] [62]
Spectral Properties for a class of continuous state branching processes with immigration, J. Funct. Anal., Vol. 201, No. 1, 185-227, 2003. [63]
On transition semigroups of (A ,Psi)- superprocesses with immigration, Ann. Probab., Vol. 31, No. 3, 1377-1412, 2003. [64]
L1-Uniqueness of regularized 2D-Euler and Stochastic Navier-Stokes Equations, J. Funct. Anal., Vol. 200, No.1,  101-117, 2003. [65]
with V.I. Bogachev, M. Röckner: Uniqueness of solutions for elliptic equations and uniqueness of invariant measures of diffusions. Mat. Sb. [66], Vol. 193, No. 7, 3-36. [67] 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. [68]
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. [69]
On the Validity of the Log-Sobolev inequality for symmetric Fleming-Viot operators. Ann. Probab., Vol. 28, No. 2, 667-684, 2000. [70]
(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. [71]
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. [72]
Dirichlet Forms and Markov Processes: A Generalized Framework including both Elliptic and Parabolic Cases, Potential Analysis, Vol. 8, No. 1, 21-60, 1998. [73]
First Order Perturbations of Dirichlet Operators: Existence and Uniqueness, J. Funct. Anal., Vol. 141, No. 1, 216-248, 1996. [74]
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. [75]
Generalized Dirichlet forms and associated Markov processes, C. R. Acad. Sci. Paris, t. 319, 1063-1068, 1994. [76]
C.L. Epstein, R. Mazzeo, ''Degenerate Diffusion Operators Arising in Population Biology'', Jahresber Dtsch Math-Ver, 2015. [77]
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. [78]
Unveröffentlichte Preprints
with Y. Shen, K. Obermayer, Risk-sensitive Markov Control Processes with strictly convex risk maps, arXiv:1403.3321 [79].
Stability of travelling waves in stochastic bistable reaction diffusion equations, arXiv:1404.3853 [80].
Stability of travelling waves in stochastic Nagumo equations, preprint arXiv:1301.6378 [81].
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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