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THE CAUCHY PROBLEM FOR THE WAVE EQUATION WITH LÉVY NOISE INITIAL DATA

Center of Mathematics for Applications (CMA), Department of Mathematics, University of Oslo, Box 1053, Blindern, N-0316 Oslo, Norway

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FRANK PROSKE

Center of Mathematics for Applications (CMA), Department of Mathematics, University of Oslo, Box 1053, Blindern, N-0316 Oslo, Norway

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, and

MIKAEL SIGNAHL

Center of Mathematics for Applications (CMA), Department of Mathematics, University of Oslo, Box 1053, Blindern, N-0316 Oslo, Norway

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https://doi.org/10.1142/S0219025706002330Cited by:2 (Source: Crossref)

Abstract

In this paper we study the Cauchy problem for the wave equation with spacetime Lévy noise initial data in the Kondratiev space of stochastic distributions. We prove that this problem has a strong and unique C²-solution, which takes an explicit form. Our approach is based on the use of the Hermite transform.

Keywords:

AMSC: 60H15, 60H40, 60G51, 60G57, 60G60, 35R60

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