Theoretical analysis of numerical schemes for stochastic differential equations

The present thesis deals with the design of an Euler-Maruyama method for stochastic differential equations (SDEs) with distributional drifts—generalized functions—and study its convergence rate. We obtain a lower bound for the convergence rate for SDEs, and for SDEs of McKean-Vlasov type using a transformation based on the mild solution of partial differential equations (PDEs). One novelty is the usage of the solution to the associated Fokker-Planck PDE in the solution of the McKean equation.