Invariant measures and random attractors of stochastic delay differential equations in Hilbert space

Li Shangzhi and Guo Shangjiang: Invariant measures and random attractors of stochastic delay differential equations in Hilbert space. (2022)

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Abstract

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.

Item Type: Journal
Publication full: Electronic journal of qualitative theory of differential equations
Date: 2022
Number: 56
ISSN: 1417-3875
Language: English
DOI: 10.14232/ejqtde.2022.1.56
Uncontrolled Keywords: Differenciálegyenlet - késleltetett, Hilbert-tér
Additional Information: Bibliogr.: p. 23-25. ; összefoglalás angol nyelven
Subjects: 01. Natural sciences
01. Natural sciences > 01.01. Mathematics
Date Deposited: 2023. Mar. 13. 11:45
Last Modified: 2023. Mar. 13. 11:45
URI: http://acta.bibl.u-szeged.hu/id/eprint/78341

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