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Stochastic shell models driven by a multiplicative fractional Brownian-motion

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Autor: Bessaih, Hakima
Garrido Atienza, María José
Schmalfuss, Björn
Departamento: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Fecha: 2016-04-15
Publicado en: Physica D: Nonlinear Phenomena, 320, 38-56.
Tipo de documento: Artículo
Resumen: We prove existence and uniqueness of the solution of a stochastic shell--model. The equation is driven by an infinite dimensional fractional Brownian--motion with Hurst--parameter H∈(1/2,1), and contains a non--trivial coefficient in front of the noise which satisfies special regularity conditions. The appearing stochastic integrals are defined in a fractional sense. First, we prove the existence and uniqueness of variational solutions to approximating equations driven by piecewise linear continuous noise, for which we are able to derive important uniform estimates in some functional spaces. Then, thanks to a compactness argument and these estimates, we prove that these variational solutions converge to a limit solution, which turns out to be the unique pathwise mild solution associated to the shell--model with fractional noise as driving process.
Cita: Bessaih, H., Garrido Atienza, M.J. y Schmalfuss, B. (2016). Stochastic shell models driven by a multiplicative fractional Brownian-motion. Physica D: Nonlinear Phenomena, 320, 38-56.
Tamaño: 324.1Kb
Formato: PDF

URI: http://hdl.handle.net/11441/43248

DOI: 10.1016/j.physd.2016.01.008

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