#### Conference abstracts

Session A7 - Stochastic Computation

July 10, 17:00 ~ 17:25

## On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions

### ETH Zurich, Switzerland   -   diyora.salimova@sam.math.ethz.ch

In this talk we show that for every arbitrarily slow convergence speed and every natural number $d \in \{ 2, 3, ... \}$ there exist stochastic differential equations with infinitely often differentiable and globally bounded coefficients such that no approximation method based on finitely many observations of the driving Brownian motion can converge in absolute mean to the solution faster than the given speed of convergence.

Joint work with Máté Gerencsér (Institute of Science and Technology, Austria) and Arnulf Jentzen (ETH Zurich, Switzerland).

FoCM 2017, based on a nodethirtythree design.