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 study the existence of moments and the tail behaviour of the densities of storage processes. We give sufficient conditions for existence and non-existence of moments using the integrability conditions of submultiplicative functions with respect to Levy measures. Then, we study the...