Elliptic equations and Gaussian processes

AbstractWe consider a Gaussian process P on s(Rd) generated by a polynomial in the Laplace operator. We prove some support properties for P. As a byproduct we strenghten earlier results on the stochastic Dirichlet problem on bounded regions Λ ⊂ Rd. We describe in this way the conditional P-distribution of the restriction to Λ of s(Rd), supposing ϑ is known outside Λ: a somewhat detailed description of the singularity of ϑ on Λ is given