Preprint:
Level Sets of the Stochastic Wave Equation Driven by
a Symmetric Lévy Noise
D. Khoshnevisan and E. Nualart
Abstract.
We consider the solution {u(t,x); t >0, x ∈ R}
of a system of d linear stochastic wave equations driven
by a d dimensional symmetric spacetime Lévy noise.
We provide a necessary and sufficient condition, on the characteristic
exponent of the Lévy noise, which describes exactly when the zero set
of u is nonvoid. We also compute the
Hausdorff dimension of that zero set, when it is nonempty.
These results will follow from more general potentialtheoretic
theorems on level sets of Lévy sheets.
Keywords.
Level sets, stochastic wave equation, Lévy noise, potential theory.
AMS Classification (2000)
Primary: 60G60, 60H15; Secondary: 60J45, 60G17.
Support.
 The research of D.K. was supported in part by a grant from
the United States National Science Foundation.
Pre/EPrints. This paper is available in
Davar Khoshnevisan
Department of Mathematics
University of Utah
155 S, 1400 E JWB 233
Salt Lake City, UT 841120090, U.S.A.
davar@math.utah.edu

Eulalia Nualart
Institut Galilée
Université Paris 13
93430 Villetaneuse, France
nualart@math.univparis13.fr

Updates: September 20, 2007
© 2007  Davar Khoshnevisan and Eulalia Nualart