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

First available in Project Euclid: 13 July 2004

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

Lévy processes white noise analysis stochastic partial differential equations


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.

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