3 citations · 6 across the 7 of their papers we have counts for
8 papers
Numerical approximation of probabilistically weak and strong solutions of the stochastic total variation flow
Ľubomír Baňas, Martin Ondreját
We propose a fully practical numerical scheme for the simulation of the stochastic total variation flow (STFV). The approximation is based on a stable time-implicit finite element…
Numerical Approximation of Nonlinear SPDE's
Martin Ondrejat, Andreas Prohl, Noel Walkington
The numerical analysis of stochastic parabolic partial differential equations of the form is surveyed, where is a partial operator and a…
Uniqueness of the nonlinear Schrödinger Equation driven by jump processes
Erika Hausenblas, Anne de Bouard, Martin Ondrejat
In a recent paper by the first two named authors, existence of martingale solutions to a stochastic nonlinear Schrödinger equation driven by a Lévy noise was proved. In this paper,…
The nonlinear Schrödinger Equation driven by jump processes
Anne de Bouard, Erika Hausenblas
The main result of the paper is the existence of a solution of the nonlinear Schrödinger equation with a \levy noise with infinite activity. To be more precise, let be the La…
Invariant measure for the stochastic Navier-Stokes equations in unbounded 2D domains
Zdzisław Brzeźniak, Elżbieta Motyl, Martin Ondrejat
Building upon a recent work by two of the authours and J. Seidler on bw-Feller property for stochastic nonlinear beam and wave equations, we prove the existence of an invariant mea…
Ergodicity for a stochastic geodesic equation in the tangent bundle of the 2D sphere
L'ubomír Banas, Zdzisław Brzeźniak, Misha Neklyudov +2
We study ergodic properties of stochastic geometric wave equations on a particular model with the target being the 2D sphere while considering the space variable-independent soluti…
Weak characterizations of stochastic integrability and Dudley's theorem in infinite dimensions
Martin Ondrejat, Mark Veraar
In this paper we consider stochastic integration with respect to cylindrical Brownian motion in infinite dimensional spaces. We study weak characterizations of stochastic integrabi…
Attractivity, invariance and ergodicity for SDEs on Riemannian manifolds
Lubomir Banas, Zdzislaw Brzezniak, Martin Ondrejat +1
We give a sufficient condition on nonlinearities of an SDE on a compact connected Riemannian manifold which implies that laws of all solutions converge weakly to the normalized…