70 citations · 150 across the 39 of their papers we have counts for
20 papers · 1 filter
A stochastic Schauder-Tychonoff type theorem and its applications
Erika Hausenblas, Ankit Kumar, Jonas M. Tölle
One standard way to prove existence for deterministic, highly nonlinear PDEs is to use the Schauder-Tychonoff fixed-point theorem. In what follows, we introduce and verify a stocha…
Yamada-Watanabe uniqueness results for SPDEs driven by Wiener and pure jump processes
Kistosil Fahim, Erika Hausenblas, Kenneth H. Karlsen
The Yamada-Watanabe theory provides a robust framework for understanding stochastic equations driven by Wiener processes. Despite its comprehensive treatment in the literature, the…
A Meta Theorem for nonlinear stochastic coupled systems: Application to stochastic chemotaxis-Stokes porous media
Erika Hausenblas, Boris Jidjou Moghomye
The purpose of the paper is twofold. Firstly, we want to present a Meta Theorem to show the existence of a martingale solution for coupled systems of non-linear stochastic differen…
A Schauder-Tychonoff fixed-point approach for nonlinear Lévy driven reaction-diffusion systems
Erika Hausenblas, Michael A. Högele, Fahim Kistosil
We show a stochastic version of the Schauder-Tychonoff fixed point theorem which yields a solution of the martingale problem for a class of systems of nonlinear reaction-diffusion…
On Markovian semigroups of Lévy driven SDEs, symbols and pseudo--differential operators
Pani W. Fernando, K. Fahim, Erika Hausenblas
We analyse analytic properties of nonlocal transition semigroups associated with a class of stochastic differential equations (SDEs) in driven by pure jump--type Lév…
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,…