论文标题
具有乘法噪声的随机微分方程的固定溶液的大偏差原理
Large deviations principle for stationary solutions of stochastic differential equations with multiplicative noise
论文作者
论文摘要
我们研究了通过弱收敛方法以无限时间间隔的一类随机微分方程（SDE）的固定溶液研究大偏差原理（LDP），然后通过收缩原则为SDE的不变度度量建立LDP。我们进一步指出，LDP的速率函数对于由LDP引起的固定溶液诱导的不变量度以及准利率定义的速率函数。这个事实给出了弗雷德林和温泽尔引入的准潜电的另一种观点。
We study the large deviations principle (LDP) for stationary solutions of a class of stochastic differential equations (SDE) in infinite time intervals by the weak convergence approach, and then establish the LDP for the invariant measures of the SDE by the contraction principle. We further point out the equivalence of the rate function of the LDP for invariant measures induced by the LDP for stationary solutions and the rate function defined by quasi-potential. This fact gives another view of the quasi-potential introduced by Freidlin and Wentzell.
