Authors:G.Benfatto, G.Gallavotti, F.Nicol\`o

Title: Elliptic equations and gaussian processes

Journal of Functional Analysis, 36, 343--400, 1980

Abstract: We consider a Gaussian process $P$ on ${\cal S}'(R^d)$ generated by a polynonial in the Laplace operator. We prove some support properties for $P$. As a byproduct we strengthen earlier results on the stochastic Dirichlet problem on bounded regions $\Lambda\subset R^d$. We describe in this way the conditional $P$-distribution of the restriction to $\Lambda$ of $\varphi\in {\cal S}'(R^d)$, supposing $\varphi$ is known outside $\Lambda$: a somewhat detailed description of the singularity of $\varphi$ onn $\Lambda$ is given.
Giovanni Gallavotti