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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Detalles Bibliográficos
Autores: Hinojosa Calleja, Adrián, Sanz-Solé, Marta
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2021
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/174485
Acceso en línea:https://hdl.handle.net/2445/174485
Access Level:acceso abierto
Palabra clave:Processos estocàstics
Anàlisi estocàstica
Stochastic processes
Analyse stochastique
Descripción
Sumario: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.