Effective fluctuating continuum models for stochastic gradient descent

Published · BIT : numerical mathematics, 60 (2020) 4, pp. 1057-1073. Optimal upper and lower error estimates for strong full-discrete numerical approximations of the stochastic heat equation driven by space-time white noise are obtained. In particular, we establish the optimality of strong convergence…

Published · Journal of theoretical probability, 33 (2020) 2, pp. 611-648. We consider finite dimensional rough differential equations driven by centered Gaussian processes. Combining Malliavin calculus, rough paths techniques and interpolation inequalities, we establish upper bounds on the density of the corresponding solution…

Published · The annals of probability, 45 (2017) 2, pp. 1325-1350. We provide sufficient conditions for weak synchronization by noise for order-preserving random dynamical systems on Polish spaces. That is, under these conditions we prove the existence of a weak point attractor consisting…