Conservative stochastic PDE and fluctuations of the symmetric simple exclusion process

no code implementations • 3 Dec 2020 • Nicolas Dirr, Benjamin Fehrman, Benjamin Gess

In the small-noise limit, we show that the fluctuations of the solutions are to first-order the same as the fluctuations of the particle system.

Probability Analysis of PDEs

Convergence rates for the stochastic gradient descent method for non-convex objective functions

no code implementations • 2 Apr 2019 • Benjamin Fehrman, Benjamin Gess, Arnulf Jentzen

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.

BIG-bench Machine Learning