论文标题
在不断发展的riemannian歧管中，布朗运动的大偏差很大
Large deviations for Brownian motion in evolving Riemannian manifolds
论文作者
论文摘要
我们证明了$ g（t）$ - 布朗的大偏差，以完整的，不断发展的Riemannian歧管$ m $相对于收集$ \ {g（t）\} _ {t \ in [0,1]} $ riemannian Mentrics的$ {t \ in [0,1]} $，取决于$ t $。我们展示了如何从$ g（t）$的（t）$ - 布朗尼运动对$ m $ $ m $ $ fm $ $ fm $的（t）$ g（t）$的水平升力的大偏差中获得的大偏差。通过将框架捆绑到一些欧几里得空间中，并将弗雷德林 - 温泽尔理论应用于时间依赖的系数中，该系数在空间和时间上共同lipschitz来证明后者。
We prove large deviations for $g(t)$-Brownian motion in a complete, evolving Riemannian manifold $M$ with respect to a collection $\{g(t)\}_{t\in [0,1]}$ of Riemannian metrics, smoothly depending on $t$. We show how the large deviations are obtained from the large deviations of the (time-dependent) horizontal lift of $g(t)$-Brownian motion to the frame bundle $FM$ over $M$. The latter is proved by embedding the frame bundle into some Euclidean space and applying Freidlin-Wentzell theory for diffusions with time-dependent coefficients, where the coefficients are jointly Lipschitz in space and time.
