Stochastic partial differential equations driven by Levy space-time white noise

Details Stochastic partial differential equations driven by Levy space-time white noise Stochastic partial differential equations driven by Levy space-time white noise

2004-07-08

arxiv.org/abs/math/0407131v1

Annals of Probability 2004, Vol. 14, No. 3, 1506-1528

Mathematics

Probability

Scientific paper

10.1214/105051604000000413

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\leq 3, then this solution can be represented as a classical random field in L2(\mu ), where \mu is 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.

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