Published · Archive for rational mechanics and analysis, 242 (2021) 1, pp. 179-234. We prove the existence of nonnegative martingale solutions to a class of stochastic degenerate-parabolic fourth-order PDEs arising in surface-tension driven thin-film flow influenced by thermal noise. The construction applies to a range…
Published · Communications in mathematical physics, 407 (2026) 4, p. 74. In this paper, we provide a continuum model for the fluctuations of the symmetric simple exclusion process about its hydrodynamic limit. The model is based on an approximating sequence of stochastic PDEs…
Published · Annales de l’Institut Henri Poincaré / B : Probabilites et statistiques, 57 (2021) 4, pp. 2354-2371. The existence of martingale solutions for stochastic porous media equations driven by nonlinear multiplicative space-time white noise is established in spatial dimension one. The Stroock-Varopoulos inequality is identified as a key tool…
Published · Workshop on Integration of Deep Neural Models and Differential Equations at ICLR 2020. Recently, progress has been made in the application of neural networks to the numerical analysis of partial differential equations (PDEs). In the latter the variational formulation of the Poisson problem is used…
Published · Inventiones mathematicae, 234 (2023) 2, pp. 573-636. Large deviations of conservative interacting particle systems, such as the zero range process, about their hydrodynamic limit and their respective rate functions lead to the analysis of the skeleton equation; a degenerate…
Published · Workshop on Integration of Deep Neural Models and Differential Equations at ICLR 2020. Residual networks (ResNets) are a deep learning architecture that substantially improved the state of the art performance in certain supervised learning tasks. Since then, they have received continuously growing attention. ResNets have…
Published · Stochastics and Dynamics 20(6), 2040006 (2020). We prove uniform synchronisation by noise with rates for the stochastic quantisation equation in dimensions two and three. The proof relies on a combination of coming down from infinity estimates and the…
Published · Journal of differential equations, 269 (2020) 4, pp. 3414-3455. We prove the existence of random dynamical systems and random attractors for a large class of locally monotone stochastic partial differential equations perturbed by additive Lévy noise. The main result is applicable…
Published · SIAM journal on mathematical analysis, 52 (2020) 5, pp. 4524-4564. The long time behaviour of solutions to stochastic porous media equations on smooth bounded domains with Dirichlet boundary data is studied. Based on weighted $L^{1}$-estimates the existence and uniqueness of invariant measures…
Published · Stochastic processes and their applications, 130 (2020) 12, pp. 7260-7302. We consider the stochastic thin-film equation with colored Gaussian Stratonovich noise in one space dimension and establish the existence of nonnegative weak (martingale) solutions. The construction is based on a Trotter-Kato-type decomposition…
Published · Nonlinear analysis / A, 187 (2019), pp. 259-278. The existence and uniqueness of measure-valued solutions to stochastic nonlinear, non-local Fokker-Planck equations is proven. This type of stochastic PDE is shown to arise in the mean field limit of weakly interacting…
Published · Journal of machine learning research, 21 (2020) 136, pp. 1-48. We prove the local convergence to minima and estimates on the rate of convergence for the stochastic gradient descent method in the case of not necessarily globally convex nor contracting objective functions…
