The Cauchy problem for the wave equation with Lévy noise initial data

Øksendal, Bernt; Proske, Frank; Signahl, Mikael
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Year
2009
Permanent link
http://urn.nb.no/URN:NBN:no-23434

Is part of
Preprint series. Pure mathematics
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Abstract
In this paper we study the Cauchy problem for the wave equation with space-time 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.