78 citations · 667 across the 41 of their papers we have counts for
41 papers
Stability of travelling wave solutions to reaction-diffusion equations driven by additive noise with Hölder continuous paths
Amjad Saef, Wilhelm Stannat
In this paper we investigate stability of travelling wave solutions to a class of reaction-diffusion equations perturbed by infinite-dimensional additive noise with Hölder continuo…
Stochastic Reaction-Diffusion Systems in Biophysics: Towards a Toolbox for Quantitative Model Evaluation
Gregor Pasemann, Carsten Beta, Wilhelm Stannat
We develop a statistical toolbox for a quantitative model evaluation of stochastic reaction-diffusion systems modeling space-time evolution of biophysical quantities on the intrace…
Approximation of Optimal Feedback Controls for Stochastic Reaction-Diffusion Equations
Wilhelm Stannat, Alexander Vogler
In this paper we present a method to approximate optimal feedback controls for stochastic reaction-diffusion equations. We derive two approximation results providing the theoretica…
Neural Network Approximation of Optimal Controls for Stochastic Reaction-Diffusion Equations
Wilhelm Stannat, Alexander Vogler, Lukas Wessels
We present a numerical algorithm that allows the approximation of optimal controls for stochastic reaction-diffusion equations with additive noise by first reducing the problem to…
Analysis of the Ensemble Kalman--Bucy Filter for correlated observation noise
Sebastian Ertel, Wilhelm Stannat
Ensemble Kalman--Bucy filters (EnKBFs) are an important tool in Data Assimilation that aim to approximate the posterior distribution for continuous time filtering problems using an…
Analysis of the feedback particle filter with diffusion map based approximation of the gain
Sahani Pathiraja, Wilhelm Stannat
Control-type particle filters have been receiving increasing attention over the last decade as a means of obtaining sample based approximations to the sequential Bayesian filtering…
Peng's Maximum Principle for Stochastic Partial Differential Equations
Wilhelm Stannat, Lukas Wessels
We extend Peng's maximum principle for semilinear stochastic partial differential equations (SPDEs) in one space-dimension with non-convex control domains and control-dependent dif…
Stability and moment estimates for the stochastic singular -Laplace equation
Florian Seib, Wilhelm Stannat, Jonas M. Tölle
We study stability, long-time behavior and moment estimates for stochastic evolution equations with additive Wiener noise and with singular drift given by a divergence type quasili…
Analytic theory of Itô-stochastic differential equations with non-smooth coefficients
Haesung Lee, Wilhelm Stannat, Gerald Trutnau
We present a detailed analysis of non-degenerate time-homogeneous Itô-stochastic differential equations with low local regularity assumptions on the coefficients. In particular the…
Mean field limit of Ensemble Square Root Filters -- discrete and continuous time
Theresa Lange, Wilhelm Stannat
Consider the class of Ensemble Square Root filtering algorithms for the numerical approximation of the posterior distribution of nonlinear Markovian signals partially observed with…
McKean-Vlasov SDEs in nonlinear filtering
Sahani Pathiraja, Sebastian Reich, Wilhelm Stannat
Various particle filters have been proposed over the last couple of decades with the common feature that the update step is governed by a type of control law. This feature makes th…
Diffusivity Estimation for Activator-Inhibitor Models: Theory and Application to Intracellular Dynamics of the Actin Cytoskeleton
Gregor Pasemann, Sven Flemming, Sergio Alonso +2
A theory for diffusivity estimation for spatially extended activator-inhibitor dynamics modelling the evolution of intracellular signaling networks is developed in the mathematical…
Fluctuation limits for mean-field interacting nonlinear Hawkes processes
Sophie Heesen, Wilhelm Stannat
We investigate the asymptotic behaviour of networks of interacting non-linear Hawkes processes modeling a homogeneous population of neurons in the large population limit. In partic…
On the continuous time limit of Ensemble Square Root Filters
Theresa Lange, Wilhelm Stannat
We provide a continuous time limit analysis for the class of Ensemble Square Root Filter algorithms with deterministic model perturbations. In the particular linear case, we specif…
Deterministic Control of Stochastic Reaction-Diffusion Equations
Wilhelm Stannat, Lukas Wessels
We consider the control of semilinear stochastic partial differential equations (SPDEs) via deterministic controls. In the case of multiplicative noise, existence of optimal contro…
Drift Estimation for Stochastic Reaction-Diffusion Systems
Gregor Pasemann, Wilhelm Stannat
A parameter estimation problem for a class of semilinear stochastic evolution equations is considered. Conditions for consistency and asymptotic normality are given in terms of gro…
On the continuous time limit of the Ensemble Kalman Filter
Theresa Lange, Wilhelm Stannat
We present recent results on the existence of a continuous time limit for Ensemble Kalman Filter algorithms. In the setting of continuous signal and observation processes, we apply…
Weak Solutions to Vlasov-McKean Equations under Lyapunov-Type Conditions
Sima Mehri, Wilhelm Stannat
We present a Lyapunov type approach to the problem of existence and uniqueness of general law-dependent stochastic differential equations. In the existing literature most results c…
Existence, uniqueness and stability of semi-linear rough partial differential equations
Peter Friz, Torstein Nilssen, Wilhelm Stannat
We prove well-posedness and rough path stability of a class of linear and semi-linear rough PDE's on using the variational approach. This includes well-posedness of…
Propagation of Chaos for Stochastic Spatially Structured Neuronal Networks with Delay driven by Jump Diffusions
Sima Mehri, Michael Scheutzow, Wilhelm Stannat +1
Spatially structured neural networks driven by jump diffusion noise with monotone coefficients, fully path dependent delay and with a disorder parameter are considered. Well-posedn…
Generalized Burgers equation with rough transport noise
Antoine Hocquet, Torstein Nilssen, Wilhelm Stannat
We introduce a new technique for studying well posedness and energy estimates for evolution equations with a rough transport term. The technique is based on finding suitable space-…
A Multiscale-Analysis of Stochastic Bistable Reaction-Diffusion Equations
Jennifer Krüger, Wilhelm Stannat
A multiscale analysis of 1D stochastic bistable reaction-diffusion equations with additive noise is carried out w.r.t. travelling waves within the variational approach to stochasti…
A complete mean-field theory for dynamics of binary recurrent neural networks
Farzad Farkhooi, Wilhelm Stannat
We develop a unified theory that encompasses the macroscopic dynamics of recurrent interactions of binary units within arbitrary network architectures. Using the martingale theory,…
Long-time stability and accuracy of the ensemble Kalman-Bucy filter for fully observed processes and small measurement noise
Jana de Wiljes, Sebastian Reich, Wilhelm Stannat
The ensemble Kalman filter has become a popular data assimilation technique in the geosciences. However, little is known theoretically about its long term stability and accuracy. I…