FoCM 2014 conference

Workshop C6 - Stochastic Computation

December 20, 14:30 ~ 15:00 - Room C11

## On a SDE with no polynomial convergence rate for strong approximation at the final time

### Larisa Yaroslavtseva

### University of Passau, Germany - larisa.yaroslavtseva@uni-passau.de

We consider the problem of strong approximation of the solution of a stochastic differential equation (SDE) at the final time based on point evaluations of the driving Brownian motion at a uniform grid. We present an example of a SDE with smooth and bounded coefficients for which no sequence of such approximations can achieve a polynomial rate of convergence. This generalizes a result from [1], which only covers the Euler scheme.

[1] Hairer,M., Hutzenthaler,M., Jentzen,A., Loss of regularity for Kolmogorov equations, Annals of Probability (to appear).

Joint work with Thomas Mueller-Gronbach (University of Passau, Germany).