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...
| Autores: | , |
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| 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 |
| 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. |
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