论文标题
Freidlin-WentCell定理的概括性关于哈密顿系统的平均
A generalization of the Freidlin-Wentcell theorem on averaging of Hamiltonian systems
论文作者
论文摘要
在本文中，我们将经典的弗雷德林·韦泽尔定理概括为汉密尔顿系统的随机扰动。 In stead of the two-dimensional standard Brownian motion, the coefficient for the noise term is no longer the identity matrix but a state-dependent matrix plus a state-dependent matrix that converges uniformly to 0 on any compact sets as $ε$ tends to 0. We also take the drift term into consideration where the drfit term also contains two parts, the state-dependent mapping and a state-dependent mapping that converges uniformly to 0 on任何紧凑型集合为$ε$都趋向于0。在证明中，我们使用广义差异操作员的结果。我们还通过构建辅助过程并将Girsanov定理应用于粘合条件的证明，以证明边缘内部弱收敛的新方法。
In this paper, we generalize the classical Freidlin-Wentzell's theorem for random perturbations of Hamiltonian systems. In stead of the two-dimensional standard Brownian motion, the coefficient for the noise term is no longer the identity matrix but a state-dependent matrix plus a state-dependent matrix that converges uniformly to 0 on any compact sets as $ε$ tends to 0. We also take the drift term into consideration where the drfit term also contains two parts, the state-dependent mapping and a state-dependent mapping that converges uniformly to 0 on any compact sets as $ε$ tends to 0. In the proof, we use the result of generalized differential operator. We also adapt a new way to prove the weak convergence inside the edge by constructing an auxiliary process and apply Girsanov's theorem in the proof of gluing condition.
