Numerical Approximations of Stochastic Differential Equations with Non-Standard Coefficients

A new generation of stochastic gradient decent algorithms can be efficient in finding global minimizers of possibly complicated, high-dimensional landscapes under suitable regularity assumptions for the gradient. The convergence analysis of such algorithms is linked to the study of ergodic properties for a particular class of stochastic differential equations (SDEs), so-called Langevin SDEs. The main focus of this project is the study of this class of SDEs and the nonasymptotic convergence analysis of the resulting algorithms with applications in machine learning and AI.