当前位置: X-MOL 学术Stoch. Process. their Appl. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Averaging principle for stochastic differential equations in the random periodic regime
Stochastic Processes and their Applications ( IF 1.4 ) Pub Date : 2021-05-10 , DOI: 10.1016/j.spa.2021.04.017
Kenneth Uda

We present the validity of stochastic averaging principle for non-autonomous slow–fast stochastic differential equations (SDEs) whose fast motions admit random periodic solutions. Our investigation is motivated by some problems arising from multi-scale stochastic dynamical systems, where configurations are time dependent due to nonlinearity of the underlying vector fields and the onset of time dependent random invariant sets. Averaging principle with respect to uniform ergodicity of the fast motion is no longer available in this scenario. The ergodicity of time periodic measures of the fast motion on certain minimal Poincaré section is used to identify the averaging limit.



中文翻译:

随机周期状态下随机微分方程的平均原理

我们提出了随机平均原理对非自治慢速快速随机微分方程(SDE)的有效性,该方程的快速运动允许随机周期解。我们的研究是由多尺度随机动力学系统引起的一些问题引起的,这些系统由于底层矢量场的非线性和与时间有关的随机不变集的出现而使配置与时间有关。在这种情况下,关于快速运动的均匀遍历性的平均原理不再可用。在某些最小庞加莱截面上,快速运动的时间周期量度的遍历性用于识别平均极限。

更新日期:2021-05-11
down
wechat
bug