标题： 适用于仿射随机泛函微分方程的广义Ornstein-Uhlenbeck过程及其应用 显示英文标题

标题： Generalized Ornstein-Uhlenbeck process for affine stochastic functional differential equations and its applications

摘要： 本文研究了仿射随机泛函微分方程的广义Ornstein-Uhlenbeck过程的存在性和全局稳定性。建立了各种非常基本且重要的性质。在应用中，我们提出了一种标准且严格的程序，以保证非线性随机泛函微分方程随机平衡解的存在性和唯一性，该程序能够吸引不同类型的收敛中的所有拉回轨迹。给出了一些例子来说明我们的主要结果。本文提出的结论改进并简化了Jiang和Lv [{\it SIAM J. 控制优化}, 54 (2016), pp. 2383-2402] 和 [{\it J. 微分方程}, 367 (2023), pp. 890-921] 的结论。 显示英文摘要

摘要： This paper studies the existence and global stability of generalized Ornstein-Uhlenbeck process for affine stochastic functional differential equations. Various very basic and important properties are established. In the applications, we present a standard and rigorous procedure for guaranteeing the existence and uniqueness 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. The results presented in this paper improve and simplify the conclusions of Jiang and Lv [{\it SIAM J. Control Optim.}, 54 (2016), pp. 2383-2402] and [{\it J. Differential Equations}, 367 (2023), pp. 890-921].