39 citations · 142 across the 19 of their papers we have counts for
11 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…
Stochastic evolution equations with nonlinear diffusivity, recent progress and critical cases
Ioana Ciotir, Dan Goreac, Jonas M. Tölle
This short survey article stems from recent progress on critical cases of stochastic evolution equations in variational formulation with additive, multiplicative or gradient noises…
Variability and the existence of rough integrals with irregular coefficients
Michael Hinz, Jonas M. Tölle, Lauri Viitasaari
Within the context of rough path analysis via fractional calculus, we show how variability can be used to prove the existence of integrals with respect to Hölder continuous multipl…
Renormalized stochastic pressure equation with log-correlated Gaussian coefficients
Benny Avelin, Tuomo Kuusi, Patrik Nummi +3
We study periodic solutions to the following divergence-form stochastic partial differential equation with Wick-renormalized gradient on the -dimensional flat torus $\mathbb{T}^…
1D stochastic pressure equation with log-correlated Gaussian coefficients
Benny Avelin, Tuomo Kuusi, Patrik Nummi +3
We study unique solvability for one dimensional stochastic pressure equation with diffusion coefficient given by the Wick exponential of log-correlated Gaussian fields. We prove we…
Sobolev regularity of occupation measures and paths, variability and compositions
Michael Hinz, Jonas M. Tölle, Lauri Viitasaari
We prove a result on the fractional Sobolev regularity of composition of paths of low fractional Sobolev regularity with functions of bounded variation. The result relies on the no…
Variability of paths and differential equations with -coefficients
Michael Hinz, Jonas M. Tölle, Lauri Viitasaari
We define compositions of Hölder paths in and functions of bounded variation under a relative condition involving the path and the gradient measure of…
A compact topology for -algebra convergence
Patrick Beissner, Jonas M. Tölle
We propose a sequential topology on the space of sub--algebras of a separable probability space by linking conditional expectations on along…
Ergodicity and local limits for stochastic local and nonlocal p-Laplace equations
Benjamin Gess, Jonas M. Tölle
Ergodicity for local and nonlocal stochastic singular -Laplace equations is proven, without restriction on the spatial dimension and for all . This generalizes previo…
Convergence of invariant measures for singular stochastic diffusion equations
Ioana Ciotir, Jonas M. Tölle
It is proved that the solutions to the singular stochastic -Laplace equation, and the solutions to the stochastic fast diffusion equation with nonlinearity paramete…
Multi-valued, singular stochastic evolution inclusions
Benjamin Gess, Jonas M. Tölle
We provide an abstract variational existence and uniqueness result for multi-valued, monotone, non-coercive stochastic evolution inclusions in Hilbert spaces with general additive…