论文标题
非自主随机系统的进化系统的渐近稳定性：理论结果和应用
Asymptotic stability of evolution systems of probability measures for nonautonomous stochastic systems: Theoretical results and applications
论文作者
论文摘要
文献中广泛讨论了自主随机系统的时间均匀过渡半群的不变概率度量的限制稳定性。在本文中，我们最初启动了一个计划，以研究非自主随机系统的时间不均匀过渡算子的进化系统的渐近稳定性。通过建立一些可以在应用程序中验证的足够条件，可以在波兰空间中建立对该主题的一般理论结果。我们的抽象结果应用于由时间依赖性非线性噪声驱动的随机晶格反应扩散方程。时间平均的方法和对时间依赖性扩散函数的轻度条件用于证明每个概率测量的演化系统的极限必须是限制方程的概率测量的演化系统。预计将来，理论结果将用于各种随机晶格系统/ODES/PDE。
The limiting stability of invariant probability measures of time homogeneous transition semigroups for autonomous stochastic systems has been extensively discussed in the literature. In this paper we initially initiate a program to study the asymptotic stability of evolution systems of probability measures of time inhomogeneous transition operators for nonautonomous stochastic systems. A general theoretical result on this topic is established in a Polish space by establishing some sufficient conditions which can be verified in applications. Our abstract results are applied to a stochastic lattice reaction-diffusion equation driven by a time-dependent nonlinear noise. A time-average method and a mild condition on the time-dependent diffusion function are used to prove that the limit of every evolution system of probability measures must be an evolution system of probability measures of the limiting equation. The theoretical results are expected to be applied to various stochastic lattice systems/ODEs/PDEs in the future.
