Convolution Equation: Solution and Probabilistic Representation

摘要

In this paper we study a Cauchy problem associated to Δ_K~*, the adjoint of ΔK which is related to the Gross Laplacian for certain choice of the operator K.We show that the solution is a well defined generalized function in an appropriate space. Finally, using infinite dimensional stochastic calculus we give a probabilistic representation of the solution in terms of K-Wiener process W.