Gerencsér Máté: Discrete approximations of SDEs with irregular drift

Recent years saw increasing interest in establishing the rate of convergence of approximation schemes to solutions of stochastic differential equations (SDEs) whose drift is rough. In such situations it is crucial to exploit regularising effects of the noise.
We introduce a new take on the convergence analysis, based on the `stochastic sewing lemma', that, among others, allows one to establish strong convergence rates up to 1/2 higher for the Euler-Maruyama scheme than earlier methods, as well as to handle non-Markovian driving noise.
Joint work with O. Butkovsky and K. Dareiotis.