On the Probabilistic Representation of the Resolvent of the Two-Dimensional Laplacian
摘要
In this paper, we consider a family of random linear operators that arises in the construction of a probabilistic representation of the resolvent of the two-dimensional Laplacian. It is shown that with probability 1 the operators of this family are integral operators in L2(ℝ2). The properties of the kernels of the corresponding operators are also studied.