Stability and ergodicity of nonlinear stochastic delay differential equations
Abstract
In this paper, we consider stability and ergodicity of nonlinear stochastic delay differential equations with infinite delay on Cr. Existing results depend on linear structure or finite delay. Under the local Lipschitz condition and modified dissipative condition, we obtain the stability in distribution of the solution map xt with nonlinear distribution delay, which also admits a unique invariant measure under slightly stronger conditions. We show that the convergence rate to the invariant measure is exponential under the Wasserstein distance.
Fields of Study & Subjects
Nonlinear Differential Equations Analysis
Stability and Control of Uncertain Systems
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- Applicable Analysis
- Volume
- 105
- Issue
- 12
- Pages
- 2811–2828
- Publication date
- 30 January 2026
- Language
- EN