论文标题
连续依赖不变措施的参数及其在多尺度随机系统中的应用
Continuous dependence on parameters for invariant measures and its application to multiscale stochastic systems
论文作者
论文摘要
当快速过程不在紧凑的空间中时，完全耦合的多尺度随机系统的渐近行为变得非常复杂。构建了一个说明性的示例，该例子表明，平均系数也可能变得不连续，即使它们最初是Lipschitz的连续。我们旨在揭示快速过程对极限过程和平均原理的影响。关键点是对与瓦斯林空间各个距离的不变概率度量相关的参数的连续依赖性。
The asymptotic behavior for fully coupled multiscale stochastic systems becomes much complicated when the fast processes do not locate in a compact space. An illustrative example is constructed, which shows that the averaged coefficients may become discontinuous even they are originally Lipschitz continuous. We aim to reveal the impact of the ergodicity of the fast process on the limit process and the averaging principle. The crucial point is the continuous dependence on parameters related to the slow process for the invariant probability measures in various distances over the Wasserstein space.
