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 space-time 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 potential-theoretic
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/E-Prints. This paper is available in
Davar Khoshnevisan
Department of Mathematics
University of Utah
155 S, 1400 E JWB 233
Salt Lake City, UT 84112-0090, U.S.A.
davar@math.utah.edu
|
Eulalia Nualart
Institut Galilée
Université Paris 13
93430 Villetaneuse, France
nualart@math.univ-paris13.fr
|
Updates: September 20, 2007
© 2007 - Davar Khoshnevisan and Eulalia Nualart