78 citations · 667 across the 41 of their papers we have counts for
5 papers · 1 filter
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…
On Average Risk-sensitive Markov Control Processes
Yun Shen, Klaus Obermayer, Wilhelm Stannat
We introduce the Lyapunov approach to optimal control problems of average risk-sensitive Markov control processes with general risk maps. Motivated by applications in particular to…
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…