Consider the density of the solution $X(t,x)$ of a stochastic heat equation with small noise at a fixed $t\in [0,T]$, $x \in [0,1]$. In the paper we study the asymptotics of this density as the noise is vanishing. A kind of Taylor expansion in powers of the noise parameter is obtained. The...

We develop a general error analysis framework for the Monte Carlo simulation of densities for functionals in Wiener space. We also study variance reduction methods with the help of Malliavin derivatives. For this, we give some general heuristic principles which are applied to diffusion...