Random attractors for stochastic evolution equations driven by fractional brownian motion
The main goal of this article is to prove the existence of a random attractor for a stochastic evolution equation driven by a fractional Brownian motion with Hurst parameter H ∈ (1/2, 1). We would like to emphasize that we do not use the usual cohomology method, consisting of transforming the stocha...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/42198 |
| Acceso en línea: | http://hdl.handle.net/11441/42198 https://doi.org/10.1137/130930662 |
| Access Level: | acceso abierto |
| Palabra clave: | fractional derivatives pathwise mild solutions nonautonomous and random dynamical systems fractional Brownian motion pullback and random attractors |
| Sumario: | The main goal of this article is to prove the existence of a random attractor for a stochastic evolution equation driven by a fractional Brownian motion with Hurst parameter H ∈ (1/2, 1). We would like to emphasize that we do not use the usual cohomology method, consisting of transforming the stochastic equation into a random one, but we deal directly with the stochastic equation. In particular, in order to get adequate a priori estimates of the solution needed for the existence of an absorbing ball, we will introduce stopping times to control the size of the noise. In the first part of this article we shall obtain the existence of a pullback attractor for the nonautonomous dynamical system generated by the pathwise mild solution of an nonlinear infinitedimensional evolution equation with a nontrivial Hölder continuous driving function. In the second part, we shall consider the random setup: stochastic equations having as a driving process a fractional Brownian motion with H ∈ (1/2, 1). Under a smallness condition for that noise we will show the existence and uniqueness of a random attractor for the stochastic evolution equation. |
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