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<p>This paper studies the existence and global stability of generalized Ornstein–Uhlenbeck processes for affine stochastic functional differential equations. Various very basic and important properties are established. In the applications, we present a new and rigorous procedure for guaranteeing the existence and global stability of random equilibria for nonlinear stochastic functional differential equations, which attracts all pull-back trajectories in different types of convergence. Some examples are given to illustrate our main results.</p>

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Generalized Ornstein–Uhlenbeck Process for Affine Stochastic Functional Differential Equations and Its Applications

  • 期刊论文

  • 发表日期：

    2026年6月3日

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  • Xiang Lv

摘要

This paper studies the existence and global stability of generalized Ornstein–Uhlenbeck processes for affine stochastic functional differential equations. Various very basic and important properties are established. In the applications, we present a new and rigorous procedure for guaranteeing the existence and global stability of random equilibria for nonlinear stochastic functional differential equations, which attracts all pull-back trajectories in different types of convergence. Some examples are given to illustrate our main results.