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TU Berlin

Inhalt des Dokuments

Prof. Dr. Wilhelm Stannat

In preparation
48.
with E. Lang, Finite-Size Effects on Traveling Wave Solutions to Neural Field Equations, manuscript 2014, eingereicht.
47.
with Y. Shen, K. Obermayer, Risk-sensitive Markov Control Processes with strictly convex risk maps arXiv:1403.3321, eingereicht.
46.
Stability of travelling waves in stochastic bistable reaction diffusion equations, arXiv:1404.3853, eingereicht.
45.
with M. Sauer, Analysis and Approximation of Stochastic Nerve Axon Equations, arXiv:1402.4791, eingereicht.
44.
Stability of travelling waves in stochastic Nagumo equations, preprint arXiv:1301.6378, eingereicht.
43.
Stochastic Navier-Stokes Equations, manuscript 2011.

Accepted papers
42.
with S. Voronenko, B. Lindner,Shifting spike times or adding and deleting spikes - how different types of noise shape signal transmission in neural populations, accepted for publication in The Journal of Mathematical Neuroscience, 2014.
41.
with S. Yokoyama, Weak solutions of non-coercive stochastic Navier-Stokes equations in R2, accepted for publication in Aust. J. Math. Anal. Appl., 2014.
40.
with Y. Shen, K. Obermayer, A Unified Framework for Risk-sensitive Markov Control Processes, 53rd IEEE Conference on Decision and Control, 2014, to appear.
Publications (refereed)
39.
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.  
38.
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, Mathematics of Computation,
S 0025-5718(2014)02873-1, 24 pages, 2014.

36.
with E. Lucon, Mean Field Limit for disordered diffusions with singular interactions, Ann. Appl. Probab., Vol. 24, 1946-1993, 2014. 
35.
with Y. Shen, K. Obermayer, Risk-sensitive Markov Control Processes,  SIAM J. Control Optim., Vol. 51, 3652-3672, 2013. 
34.
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.
33.
with M. Hieber, Stochastic Stability of the Ekman Spiral, manuscript, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5), Vol. 12, 189-208, 2013.  
32.
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.  
31.
Stochastic partial differential equations: Kolmogorov operators and invariant measures, Jahresbericht der deutschen Mathematiker-Vereinigung, Vol. 113, 81-109, 2011.  
30.
Lp-Uniqueness of Kolmogorov operator associated with 2D-Stochastic Navier-Stokes -Coriolis equations, Mathematische Nachrichten, vol 284, 2287-2296, 2011.  
29.
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.  
28.
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.   
27.
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.
26.
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.   
25.
with M. Döring, The Logarithmic Sobolev inequality for the Wasserstein diffusion, Probab. Theory Relat. Fields, Vol. 145, 189-209, 2009. 
24.
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.
23.
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.
22.
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.  
21.
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.
20.
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.
19.
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.
18.
Stability of the pathwise filter equation for a time-dependent signal on Rd, in Appl.  Math. Optim., Vol. 52, No. 1, 39-71, 2005.   
17.
On the Poincare inequality for infinitely divisible measures, Potential Analysis, Vol. 23, No. 3, 279 - 301, 2005.  
16.
Time-Dependent Diffusion operators on L1, Journal of Evolution Equations, Vol. 4, No. 4, 463-495, 2004.    
15.
A remark on the CLT for a random walk in a random environment, Probab. Theory Relat. Fields, Vol. 130, No. 3, 377-387, 2004.   
14.
On the convergence of genetic algorithms - a variational approach, Probab. Theory Relat. Fields, Vol. 129, No.1, 113-132, 2004.   
13.
Spectral Properties for a class of continuous state branching processes with immigration, J. Funct. Anal., Vol. 201, No. 1, 185-227, 2003.
12.
On transition semigroups of (A ,Psi)- superprocesses with immigration, Ann. Probab., Vol. 31, No. 3, 1377-1412, 2003.
11.
L1-Uniqueness of regularized 2D-Euler and Stochastic Navier-Stokes Equations, J. Funct. Anal., Vol. 200, No.1,  101-117, 2003.
10.
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.
9.
Long-time behaviour and regularity properties of transition semigroups of Fleming-Viot processes, Probab. Theory Relat. Fields, Vol. 122, 431-469, 2002.   
8.
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.
7.
On the Validity of the Log-Sobolev inequality for symmetric Fleming-Viot operators. Ann. Probab., Vol. 28, No. 2, 667-684, 2000.
6.
(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.
5.
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.
4.
Dirichlet Forms and Markov Processes: A Generalized Framework including both Elliptic and Parabolic Cases, Potential Analysis, Vol. 8, No. 1, 21-60, 1998.
3.
First Order Perturbations of Dirichlet Operators: Existence and Uniqueness, J. Funct. Anal., Vol. 141, No. 1, 216-248, 1996.
2.
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.
1.
Generalized Dirichlet forms and associated Markov processes, C. R. Acad. Sci. Paris, t. 319, 1063-1068, 1994.
Selected Abstracts
4.
Stochastic nerve axon equations. In: Dirichlet forms and its applications, Editors: S. Albeverio, et al., Oberwolfach Reports NN, 2014.
3.
Stochastic partial differential equations in mathematical fluid dynamics. In: Geophysical Fluid Dynamics, Editors: Y. Giga, et al., Oberwolfach Reports, Vol. 10, 483–520, 2013. 
2.
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.
1.
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.
Papers in Engineering Sciences
1.
Maintaining Replicas in Unstructured Peer-to-Peer Systems (with C. Lang, W. Terpstra, B. Kemme, A.P. Buchmann) Proceedings of 2008 ACM CoNEXT Conference.
Theses
3.
Analysis of Measure-Valued Processes and Infinite Dimensional Differential Operators, Habilitationsschrift, U Bielefeld 2002.
2.
The Theory of Generalized Dirichlet Forms and Its Applications in Analysis and Stochastics, Dissertation, U Bielefeld 1996.
1.
Verallgemeinerte zeitabhängige Dirichletformen, Diplomarbeit, U Bonn 1993. 

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