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 documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2008 |
| País: | España |
| Recursos: | Universitat Pompeu Fabra |
| Repositório: | Repositorio Digital de la UPF |
| OAI Identifier: | oai:repositori.upf.edu:10230/34389 |
| Acesso em linha: | http://hdl.handle.net/10230/34389 http://dx.doi.org/10.3150/08-BEJ133 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Level sets Lévy noise Potential theory Stochastic wave equation |
| Resumo: | 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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