Artículo
Random attractors for stochastic evolution equations driven by fractional brownian motion
Autor/es | Gao, Hongjun
Garrido Atienza, María José Schmalfuss, Björn |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2014 |
Fecha de depósito | 2016-06-13 |
Publicado en |
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Resumen | 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 ... 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. |
Identificador del proyecto | 11171158
2013CB834100 BK2011777 11KJA110001 MTM2011-22411 |
Cita | Gao, H., Garrido Atienza, M.J. y Schmalfuss, B. (2014). Random attractors for stochastic evolution equations driven by fractional brownian motion. SIAM Journal on Mathematical Analysis, 46 (4), 2281-2309. |
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