Exponential behavior and upper noise excitation index of solutions to evolution equations with unbounded delay and tempered fractional Brownian motions
In this paper, we investigate stochastic evolution equations with unbounded delay in fractional power spaces perturbed by a tempered fractional Brownian motion Bσ,λQ(t) with −1/2<σ<0 and λ>0. We first introduce a technical lemma which is crucial in our stability analysis. Then, we prove the...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/116650 |
| Acceso en línea: | https://hdl.handle.net/11441/116650 https://doi.org/10.1007/s00028-020-00656-0 |
| Access Level: | acceso abierto |
| Palabra clave: | Stochastic PDEs Unbounded delay Tempered fractional Brownian motion Fractional powers of closed operators Exponential decay in mean square |
| Sumario: | In this paper, we investigate stochastic evolution equations with unbounded delay in fractional power spaces perturbed by a tempered fractional Brownian motion Bσ,λQ(t) with −1/2<σ<0 and λ>0. We first introduce a technical lemma which is crucial in our stability analysis. Then, we prove the existence and uniqueness of mild solutions by using semigroup methods. The upper nonlinear noise excitation index of the energy solutions at any finite time t is also obtained. Finally, we consider the exponential asymptotic behavior of mild solutions in mean square. |
|---|