An abstract criterion on the existence and global stability of stationary solutions for random dynamical systems and its applications
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915441370202112 |
|---|---|
| author | Lv, Xiang |
| author_facet | Lv, Xiang |
| contents | We prove a concise and easily verifiable criterion on the existence and global stability of stationary solutions for random dynamical systems (RDSs). As a consequence, we can show that the $ω$-limit sets of all pullback trajectories of semilnear/nonlinear stochastic differential equations (SDEs) with additive/multiplicative white noise are composed of nontrivial random equilibria. The proof is different from the classical RDS scheme, which was established in \cite{CKS}. Furthermore, in the applications of stability analysis for SDEs, our conditions are not only sufficient but indeed sharp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08497 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An abstract criterion on the existence and global stability of stationary solutions for random dynamical systems and its applications Lv, Xiang Dynamical Systems Probability 37H05, 60H10, 60G10, 37A30, 34C10 We prove a concise and easily verifiable criterion on the existence and global stability of stationary solutions for random dynamical systems (RDSs). As a consequence, we can show that the $ω$-limit sets of all pullback trajectories of semilnear/nonlinear stochastic differential equations (SDEs) with additive/multiplicative white noise are composed of nontrivial random equilibria. The proof is different from the classical RDS scheme, which was established in \cite{CKS}. Furthermore, in the applications of stability analysis for SDEs, our conditions are not only sufficient but indeed sharp. |
| title | An abstract criterion on the existence and global stability of stationary solutions for random dynamical systems and its applications |
| topic | Dynamical Systems Probability 37H05, 60H10, 60G10, 37A30, 34C10 |
| url | https://arxiv.org/abs/2508.08497 |