78 citations · 667 across the 41 of their papers we have counts for
28 papers · 1 filter
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…
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…
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…
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…
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…
Finite-Size Effects on Traveling Wave Solutions to Neural Field Equations
Eva Lang, Wilhelm Stannat
Neural field equations are used to describe the spatiotemporal evolution of the activity in a network of synaptically coupled populations of neurons in the continuum limit. Their h…
A Fenchel-Moreau-Rockafellar type theorem on the Kantorovich-Wasserstein space with Applications in Partially Observable Markov Decision Processes
Vaios Laschos, Klaus Obermayer, Yun Shen +1
By using the fact that the space of all probability measures with finite support can be somehow completed in two different fashions, one generating the Arens-Eells space and anothe…
-Stability of Traveling Wave Solutions to Nonlocal Evolution Equations
Eva Lang, Wilhelm Stannat
Stability of the traveling wave solution to a general class of one-dimensional nonlocal evolution equations is studied in -spaces, thereby providing an alternative approach to…
Transition from Gaussian to non-Gaussian fluctuations for mean-field diffusions in spatial interaction
Eric Luçon, Wilhelm Stannat
We consider a system of disordered mean-field interacting diffusions within spatial constraints: each particle is attached to one site of a periodic lattice and the…
Stochastic partial differential equations: a rough path view
Joscha Diehl, Peter K. Friz, Wilhelm Stannat
We discuss regular and weak solutions to rough partial differential equations (RPDEs), thereby providing a (rough path-)wise view on important classes of SPDEs. In contrast to many…
Front Propagation in Stochastic Neural Fields: A Rigorous Mathematical Framework
Jennifer Krüger, Wilhelm Stannat
We develop a complete and rigorous mathematical framework for the analysis of stochastic neural field equations under the influence of spatially extended additive noise. By compari…
Stability of travelling waves in stochastic bistable reaction-diffusion equations
Wilhelm Stannat
We extend the result on the stability of travelling waves for stochastic Nagumo equations in [St] to general bistable reaction-diffusion equations with both additive and multiplica…
Analysis and Approximation of Stochastic Nerve Axon Equations
Martin Sauer, Wilhelm Stannat
We consider spatially extended conductance based neuronal models with noise described by a stochastic reaction diffusion equation with additive noise coupled to a control variable…
Stability of the optimal filter in a hidden Markov model with multiplicative noise
Birgit Debrabant, Wilhelm Stannat
We consider a hidden Markov model with multiplicative noise emerging from studies of software reliability. We show the stability of the optimal filter with respect to general initi…
Mean field limit for disordered diffusions with singular interactions
Eric Luçon, Wilhelm Stannat
Motivated by considerations from neuroscience (macroscopic behavior of large ensembles of interacting neurons), we consider a population of mean field interacting diffusions in $\m…