Level sets of the stochastic wave equation driven by a symmetric Lévy noise

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 i...

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Detalles Bibliográficos
Autores: Khoshnevisan, Davar, Nualart, Eulàlia
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2008
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:10230/34389
Acceso en línea:http://hdl.handle.net/10230/34389
http://dx.doi.org/10.3150/08-BEJ133
Access Level:acceso abierto
Palabra clave:Level sets
Lévy noise
Potential theory
Stochastic wave equation
Descripción
Sumario: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 non-void. We also compute the Hausdorff dimension of that zero set when it is non-empty. These results will follow from more general potential-theoretic theorems on the level sets of Lévy sheets.