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August 2004 Stochastic partial differential equations driven by Lévy space-time white noise
Arne Løkka, Bernt Øksendal, Frank Proske
Ann. Appl. Probab. 14(3): 1506-1528 (August 2004). DOI: 10.1214/105051604000000413

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) Lé vy white noise. As an example we use this theory to solve the stochastic Poisson equation with respect to Lévy white noise for any dimension d. The solution is a stochastic distribution process given explicitly. We also show that if d3, then this solution can be represented as a classical random field in L2(μ), where μ is the probability law of the L évy 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 Lévy Hermite transform.

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Arne Løkka. Bernt Øksendal. Frank Proske. "Stochastic partial differential equations driven by Lévy space-time white noise." Ann. Appl. Probab. 14 (3) 1506 - 1528, August 2004. https://doi.org/10.1214/105051604000000413

Information

Published: August 2004
First available in Project Euclid: 13 July 2004

zbMATH: 1053.60069
MathSciNet: MR2071432
Digital Object Identifier: 10.1214/105051604000000413

Subjects:
Primary: 60G51 , 60H15 , 60H40

Keywords: Lévy processes , Stochastic partial differential equations , white noise analysis

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.14 • No. 3 • August 2004
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