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Title:
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Level sets of the stochastic wave equation driven by a symmetric Lévy noise
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Author:
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Khoshnevisan, Davar; Nualart, Eulàlia
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Abstract:
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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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Abstract:
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Research supported in part by the NSF Grant DMS-07-06728. |
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Subject(s):
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-Level sets
-Lévy noise
-Potential theory
-Stochastic wave equation |
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Rights:
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© 2008 ISI/BS
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Document type:
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Article
Article - Published version |
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Published by:
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International Statistical Institute, Bernoulli Society for Mathematical Statistics and Probability
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