Tail estimates for positive solutions of stochastic heat equation

Abstract

In this paper, we study the solution of a class of stochastic heat equations of convolution type. We give an explicit solution X t using two basic tools: the characterization theorem for generalized functions and the convolution calculus. For positive initial condition f and coefficients processes Vt, Mt, we prove that the corresponding solution X t admits an integral representation by a certain measure. Finally, we compute the tail estimate for the obtained solution and its expectation.