Stochastic Analysis on Noncompact Manifolds

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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.