Stochastic Partial Differential Equations driven by Lévy Space-Time White Noise

Abstract

In this paper we develop a white noise framework for the study of stochastic partial differential equations driven by a d-parameter (pure jump) Lévy white noise. As an example we use this theory to solve the stochastic Poisson equation with respect to Lévy white noise. The starting point of our theory is a chaos expansion in terms of generalized Charlier polynomials. Based on this expansion we define Kondratiev spaces and the Lévy Hermite transform.\n\nKey words and phrases: Lévy processes, white noise analysis, stochastic partial differential equations