2004/07/08 by Arne Lokka, Bernt Oksendal, Frank Proske · 1 citation
Mathematics · #math.PR #msc:60G51 #msc:60H40 #msc:60H15.
paper · pdf · doi:10.1214/105051604000000413
published as Annals of Probability 2004, Vol. 14, No. 3, 1506-1528
arxiv created 2004/07/08 · arxiv updated 2016/09/07
In this paper we develop a white noise framework for the study of stochastic partial differential equations driven by a d-parameter (pure jump) Levy white noise. As an example we use this theory to solve the stochastic Poisson equation with respect to Levy white noise for any dimension d. The solution is a stochastic distribution process given explicitly. We also show that if d≤ 3, then this solution can be represented as a classical random field in L2(μ), where μis the probability law of the Levy process. 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 Levy Hermite transform.