Effective fluctuating continuum models for stochastic gradient descent

Published · Stochastics and dynamics, 22 (2022) 7, p. 2240023. A new mechanism leading to a random version of Burgers’ equation is introduced: it is shown that the Totally Asymmetric Exclusion Process in discrete time (TASEP) can be understood as an intrinsically…

Published · Probability theory and related fields, 173 (2019) 3/4, pp. 1063-1098. We study regularizing effects of nonlinear stochastic perturbations for fully nonlinear PDE. More precisely, path-by-path $L^{\infty}$ bounds for the second derivative of solutions to such PDE are shown. These bounds are expressed…