本文考虑带小扰动的随机发展方程,证明如何建立此方程的耦合解.作为应用,我们证明解的Feller连续性和不变测度的存在唯一性.还进一步建立了当扰动趋于零时,关于这族不变测度的大偏差原理.

In this paper we consider a random evolution equation with small perturbations, and show how to construct coupled solutions to the equation. As applications, we prove the Feller continuity of the solutions and the existence and uniqueness of invariant measures. Furthermore, we establish a large deviations principle for the family of invariant measures as the perturbations tend to zero.