Stochastic shell models driven by a multiplicative fractional Brownian-motion
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....
| Autores: | , , |
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| Formato: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2016 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/43248 |
| Acesso em linha: | http://hdl.handle.net/11441/43248 https://doi.org/10.1016/j.physd.2016.01.008 |
| Access Level: | acceso abierto |
| Palavra-chave: | Stochastic PDEs Fractional Brownian-motion Pathwise solutions Fractional calculus |
| Resumo: | 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. |
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