Appears in collection : New trends of stochastic nonlinear systems: well-posedeness, dynamics and numerics / Nouvelles tendances en analyse non linéaire stochastique: caractère bien posé, dynamique et aspects numériques

I will provide a general overview on some recent results on strong and weak error rates for Euler-type schemes for SDEs with distributional drift. In particular, the classes of drift considered include elements of negative fractional Sobolev spaces or negative Besov spaces with regularity index in (-1/2, 0). After reviewing various notions of solution for this class of SDEs, we delve into the numerics. Firstly we present a two-step Euler-type scheme that has been applied to different settings (additive Brownian noise, additive fractional Brownian noise). We derive bounds for the strong error, both in the SDE case (linear) and in the McKean equation case (nonlinear). Secondly we present a different Euler-type scheme that has been used for the case of alpha-stable additive noise and derive bounds for the error of the densities (linked to the weak error) in the linear case. Finally, time permitting, we will show some numerical results.