Anisotropic Gaussian random fields: criteria for hitting probabilities and applications

We develop criteria for hitting probabilities of anisotropic Gaussian random fields with associated canonical pseudo-metric given by a class of gauge functions. This yields lower and upper bounds in terms of general notions of capacity and Hausdorff measure, respectively, therefore extending the cla...

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Detalhes bibliográficos
Autores: Hinojosa Calleja, Adrián, Sanz-Solé, Marta
Tipo de documento: artigo
Estado:Versión aceptada para publicación
Data de publicação:2021
País:España
Recursos:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositório:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/174485
Acesso em linha:https://hdl.handle.net/2445/174485
Access Level:Acceso aberto
Palavra-chave:Processos estocàstics
Anàlisi estocàstica
Stochastic processes
Analyse stochastique
Descrição
Resumo:We develop criteria for hitting probabilities of anisotropic Gaussian random fields with associated canonical pseudo-metric given by a class of gauge functions. This yields lower and upper bounds in terms of general notions of capacity and Hausdorff measure, respectively, therefore extending the classical estimates with the Bessel-Riesz capacity and the $\gamma$ -dimensional Hausdorff measure. We apply the criteria to a system of linear stochastic partial differential equations driven by space-time noises that are fractional in time and either white or colored in space.