Weak Existence and Uniqueness for Super-Brownian Motion with Irregular Drift

Published · Journal of differential equations, 266 (2019) 6, pp. 3732-3763. We provide an entropy formulation for porous medium-type equations with a stochastic, non-linear, spatially inhomogeneous forcing. Well – posedness and $L_1$-contraction is obtained in the class of entropy solutions. Our scope allows…

Published · Journal de mathématiques pures et appliquées, 101 (2014) 6, pp. 789-827. We provide an abstract variational existence and uniqueness result for multi-valued, monotone, non-coercive stochastic evolution inclusions in Hilbert spaces with general additive and Wiener multiplicative noise. As examples we discuss certain singular…

Published · Stochastics and partial differential equations : analysis and computations, 11 (2023) 1, pp. 211-268. The scientific literature contains a number of numerical approximation results for stochastic partial differential equations (SPDEs) with superlinearly growing nonlinearities but, to the best of our knowledge, none of them prove strong…

Published · The annals of applied probability, 35 (2025) 1, pp. 481-522. We study scaling limits of the weakly driven Zhang and the Bak-Tang-Wiesenfeld (BTW) model for self-organized criticality. We show that the weakly driven Zhang model converges to a stochastic partial differential equation…

Published · Journal of the European Mathematical Society, 23 (2021) 2, pp. 425-465. We prove optimal regularity for solutions to porous media equations in Sobolev spaces, based on velocity averaging techniques. In particular, the obtained regularity is consistent with the optimal regularity in the linear…