SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 1-31, January 2021.
The Onsager--Machlup (OM) and Freidlin--Wentzell (FW) functionals are both widely used in seeking the most probable transition path between two states for a diffusion process. We study the relation between these two functionals on the space of curves. We prove that the $\Gamma$-limit of the OM functional on the space of curves is the geometric form of the FW functional in a proper time scale $T=T(\epsilon)$ as $\epsilon\to 0$. For other time scales, the limit of the OM functional is infinite in general. We then introduce the concept of renormalization for the OM functional and prove that the $\Gamma$-limit of the renormalized OM functional is the geometric FW functional in any time scale on the space of curves.

中文翻译：

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曲线空间上Onsager-Machlup函数的伽马极限

SIAM数学分析杂志，第53卷，第1期，第1-31页，2021
年1月。Onsager-Machlup（OM）和Freidlin-Wentzell（FW）功能均广泛用于寻找两者之间最可能的过渡路径扩散过程的状态。我们研究曲线空间上这两个函数之间的关系。我们证明了曲线空间上OM函数的$ \ Gamma $极限是FW函数在适当时间标度$ T = T（\ epsilon）$作为$ \ epsilon \至0 $的几何形式。对于其他时间范围，OM功能的限制通常是无限的。然后，我们介绍OM函数的重新归一化的概念，并证明重新归一化的OM函数的$ \ Gamma $极限是曲线空间上任何时间尺度上的几何FW函数。