Stochastic Analysis on Noncompact Manifolds

该项目的中心主题是分析所谓的路径空间，即弯曲空间上的连续路径空间。其目的是获得一个了解它的几何形状，并获得几何分析，它和它的子空间。这些知识应用于分析更复杂的空间，如连续回路空间。研究的主要焦点将是对Lp空间的分析。几何空间上的随机微分方程将是一个主要的工具，因此也将进行研究。这个建议的重点将是路径空间上的光滑非紧，但完整的黎曼流形。

The central theme of the project is the analysis of the so called path spaces, the space of continuous paths over a curved space. The aim is to gain an understanding of its geometry and to obtain a geometric analysis for it and for its subspaces. This knowledge shall be used for the analysis of more complicated spaces such as the space of continuous loops. The main focus of the investigation will be analysis on Lp spaces. Stochastic differential equations on geometric spaces will be a primary tool and so will also be studied. The emphasis of this proposal will be path spaces over a smooth non-compact but complete Riemannian manifold.