Invariant measures and random attractors of stochastic delay differential equations in Hilbert space
This paper is devoted to a general stochastic delay differential equation with infinite-dimensional diffusions in a Hilbert space. We not only investigate the existence of invariant measures with either Wiener process or Lévy jump process, but also obtain the existence of a pullback attractor under...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2022
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Differenciálegyenlet - késleltetett, Hilbert-tér |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2022.1.56 |
| Online Access: | http://acta.bibl.u-szeged.hu/78341 |
| Tartalmi kivonat: | This paper is devoted to a general stochastic delay differential equation with infinite-dimensional diffusions in a Hilbert space. We not only investigate the existence of invariant measures with either Wiener process or Lévy jump process, but also obtain the existence of a pullback attractor under Wiener process. In particular, we prove the existence of a non-trivial stationary solution which is exponentially stable and is generated by the composition of a random variable and the Wiener shift. At last, examples of reaction-diffusion equations with delay and noise are provided to illustrate our results. |
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| ISSN: | 1417-3875 |