Zobrazeno 1 - 10
of 74
pro vyhledávání: '"Tölle, Jonas M."'
Within the context of rough path analysis via fractional calculus, we show how the notion of variability can be used to prove the existence of integrals with respect to H\"older continuous multiplicative functionals in the case of Lipschitz coefficie
Externí odkaz:
http://arxiv.org/abs/2407.06907
Autor:
Avelin, Benny, Kuusi, Tuomo, Nummi, Patrik, Saksman, Eero, Tölle, Jonas M., Viitasaari, Lauri
We study periodic solutions to the following divergence-form stochastic partial differential equation with Wick-renormalized gradient on the $d$-dimensional flat torus $\mathbb{T}^d$, \[ -\nabla\cdot\left(e^{\diamond (- \beta X) }\diamond\nabla U\rig
Externí odkaz:
http://arxiv.org/abs/2405.17195
Autor:
Avelin, Benny, Kuusi, Tuomo, Nummi, Patrik, Saksman, Eero, Tölle, Jonas M., Viitasaari, Lauri
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 well-posedness for Dirichlet, Neumann and periodic boundary data, and th
Externí odkaz:
http://arxiv.org/abs/2402.09127
Publikováno v:
Electronic Communications in Probability 29 (2024), no. 5, 1--7
We prove that the solution to the singular-degenerate stochastic fast-diffusion equation with parameter $m\in (0,1)$, with zero Dirichlet boundary conditions on a bounded domain in any spatial dimension, and driven by linear multiplicative Wiener noi
Externí odkaz:
http://arxiv.org/abs/2310.01328
Autor:
Blömker, Dirk, Tölle, Jonas M.
Publikováno v:
Stochastics and Dynamics, vol. 23, no. 05, 2350040 1--25 (2023)
We study singular limits of stochastic evolution equations in the interplay of disappearing strength of the noise and insufficient regularity, where the equation in the limit with noise would not be defined due to lack of regularity. We recover previ
Externí odkaz:
http://arxiv.org/abs/2204.09545
Publikováno v:
Electron. J. Probab. 27 (2022), no. 73, 1--29
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 notion of variability, proposed by us in the previous article [43, arXiv
Externí odkaz:
http://arxiv.org/abs/2105.06249
Publikováno v:
Journal of Differential Equations 377 (2023) 663--693
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 quasilinear diffusion operator which may not necessarily exhibit a homogeneou
Externí odkaz:
http://arxiv.org/abs/2103.03194
Publikováno v:
Ann. Inst. H. Poincar\'e Probab. Statist. 59(4): 2036-2082 (November 2023)
We define compositions $\varphi(X)$ of H\"older paths $X$ in $\mathbb{R}^n$ and functions of bounded variation $\varphi$ under a relative condition involving the path and the gradient measure of $\varphi$. We show the existence and properties of gene
Externí odkaz:
http://arxiv.org/abs/2003.11698
Autor:
Hausenblas, Erika, Tölle, Jonas M.
Publikováno v:
Potential Analysis 61 (2024), no. 2, 185--246
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 equations proposed by Klausmeier with Gaussian multiplicative noise. On the
Externí odkaz:
http://arxiv.org/abs/1912.00996
Publikováno v:
In Journal of Differential Equations 25 December 2023 377:663-693