39 citations · 142 across the 19 of their papers we have counts for
19 papers
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…
Improved regularity for the stochastic fast diffusion equation
Ioana Ciotir, Dan Goreac, Jonas M. Tölle
We prove that the solution to the singular-degenerate stochastic fast-diffusion equation with parameter , with zero Dirichlet boundary conditions on a bounded domain in…
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…
Stability and moment estimates for the stochastic singular -Laplace equation
Florian Seib, Wilhelm Stannat, Jonas M. Tölle
We study stability, long-time behavior and moment estimates for stochastic evolution equations with additive Wiener noise and with singular drift given by a divergence type quasili…
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…
The stochastic Klausmeier system and a stochastic Schauder-Tychonoff type theorem
Erika Hausenblas, Jonas M. Tölle
On the one hand, we investigate the existence and pathwise uniqueness of a nonnegative martingale solution to the stochastic evolution system of nonlinear advection-diffusion equat…
A gradient flow formulation for the stochastic Amari neural field model
Christian Kuehn, Jonas M. Tölle
We study stochastic Amari-type neural field equations, which are mean-field models for neural activity in the cortex. We prove that under certain assumptions on the coupling kernel…
Stochastic evolution equations with singular drift and gradient noise via curvature and commutation conditions
Jonas M. Tölle
We prove existence and uniqueness of solutions to a nonlinear stochastic evolution equation on the -dimensional torus with singular -Laplace-type or total variation flow-type…
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…
Nonlinear stochastic partial differential equations with singular diffusivity and gradient Stratonovich noise
Ioana Ciotir, Jonas M. Tölle
We study existence and uniqueness of a variational solution in terms of stochastic variational inequalities (SVI) to stochastic nonlinear diffusion equations with a highly singular…
Stability of solutions to stochastic partial differential equations
Benjamin Gess, Jonas M. Tölle
We provide a general framework for the stability of solutions to stochastic partial differential equations with respect to perturbations of the drift. More precisely, we consider s…
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…
Invariant measures for monotone SPDE's with multiplicative noise term
A. Es-Sarhir, M. Scheutzow, J. M. Tölle +1
We study diffusion processes corresponding to infinite dimensional semilinear stochastic differential equations with local Lipschitz drift term and an arbitrary Lipschitz diffusion…