The Annals of Applied Probability

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

Arne Løkka, Bernt Øksendal, and Frank Proske

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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.

Article information

Source
Ann. Appl. Probab., Volume 14, Number 3 (2004), 1506-1528.

Dates
First available in Project Euclid: 13 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1089736294

Digital Object Identifier
doi:10.1214/105051604000000413

Mathematical Reviews number (MathSciNet)
MR2071432

Zentralblatt MATH identifier
1053.60069

Subjects
Primary: 60G51: Processes with independent increments; Lévy processes 60H40: White noise theory 60H15: Stochastic partial differential equations [See also 35R60]

Keywords
Lévy processes white noise analysis stochastic partial differential equations

Citation

Løkka, Arne; Øksendal, Bernt; Proske, Frank. Stochastic partial differential equations driven by Lévy space-time white noise. Ann. Appl. Probab. 14 (2004), no. 3, 1506--1528. doi:10.1214/105051604000000413. https://projecteuclid.org/euclid.aoap/1089736294


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