On the Malliavin calculus for SDE's on Hilbert spaces
A stochastic system \(x^u(t)\) of particles indexed by \(u\in R^d\) is modelled by a stochastic differential equation (SDE) on a Hilbert space. If \(\pi\) is an \(R^M\)-valued bounded linear mapping on this space, the Malliavin calculus is applied to get a condition (called a `partial Hörmander condition') under which \(\pi(x(T))\) has a smooth density with respect to the Lebesgue measure of \(R^M\). Then the propagation of the absolute continuity of measures on \(R^d\) by the stochastic flow of the SDE is studied.
scientific article; zbMATH DE number 2015163