abstract:
We consider a stochastic heat equation on the spatial domain $(0,1)$ with additive space-time white noise, and we study approximation of the mild solution at a fixed time point with respect to the average $L_2$-distance. In this talk we consider algorithms, which use a total of $N$ evaluations of one-dimensional components of the driving Wiener process $W$ and we present upper and lower error bounds in terms of $N$. In particular we compare uniform with non-uniform time discretizations. |