论文标题
随机地球学
Stochastic geodesics
论文作者
论文摘要
我们以固有的方式描述了ITO平行传输提供的全局图表，即对Riemannian歧管的扩散过程的地球概念（作为能量功能的关键路径）的概括。这些随机过程不再是平滑的路径，但它们仍然是正则随机能量功能的关键点。我们考虑在紧凑的riemannian歧管以及（可能是无限的尺寸）谎言基团上的随机测量学。最后，讨论了这种随机测量学的存在问题：我们展示了如何通过前向后的随机微分方程来接近它。
We describe, in an intrinsic way and using the global chart provided by Ito's parallel transport, a generalisation of the notion of geodesic (as critical path of an energy functional) to diffusion processes on Riemannian manifolds. These stochastic processes are no longer smooth paths but they are still critical points of a regularised stochastic energy functional. We consider stochastic geodesics on compact Riemannian manifolds and also on (possibly infinite dimensional) Lie groups. Finally the question of existence of such stochastic geodesics is discussed: we show how it can be approached via forward-backward stochastic differential equations.
