Criteria for hitting probabilities with applications to systems of stochastic wave equations

We develop several results on hitting probabilities of random fields which highlight the role of the dimension of the parameter space. This yields upper and lower bounds in terms of Hausdorff measure and Bessel-Riesz capacity, respectively. We apply these results to a system of stochastic wave equat...

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Detalhes bibliográficos
Autores: Dalang, Robert C., 1961-, Sanz-Solé, Marta
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2010
País:España
Recursos:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/23395
Acesso em linha:https://hdl.handle.net/2445/23395
Access Level:acceso abierto
Palavra-chave:Probabilitats
Processos gaussians
Equacions diferencials estocàstiques
Teoria de la mesura
Probabilities
Measure theory
Gaussian processes
Stochastic differential equations
Descrição
Resumo:We develop several results on hitting probabilities of random fields which highlight the role of the dimension of the parameter space. This yields upper and lower bounds in terms of Hausdorff measure and Bessel-Riesz capacity, respectively. We apply these results to a system of stochastic wave equations in spatial dimension k >- 1 driven by a d-dimensional spatially homogeneous additive Gaussian noise that is white in time and colored in space.