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arXiv · 2508.08497

An abstract criterion on the existence and global stability of stationary solutions for random dynamical systems and its applications

Xiang Lv
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Abstract

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 $\omega$-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.

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Xiang Lv. 2025-08-11. An abstract criterion on the existence and global stability of stationary solutions for random dynamical systems and its applications. https://arxiv.org/abs/2508.08497

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