Stochastic Analysis on Noncompact Manifolds
Lead Research Organisation:
University of Warwick
Department Name: Mathematics
Abstract
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.
Organisations
Publications
Chen X
(2010)
A Poincaré inequality on loop spaces
in Journal of Functional Analysis
Chen X
(2023)
Logarithmic heat kernel estimates without curvature restrictions
in The Annals of Probability
Chen X
(2014)
Strong completeness for a class of stochastic differential equations with irregular coefficients
in Electronic Journal of Probability
Chen X
(2010)
A concrete estimate for the weak Poincaré inequality on loop space
in Probability Theory and Related Fields
Elworthy K
(2008)
An L 2 theory for differential forms on path spaces I
in Journal of Functional Analysis
Li X
(2016)
Random perturbation to the geodesic equation
in The Annals of Probability
Li X
(2011)
Lack of strong completeness for stochastic flows
in The Annals of Probability
Li X
(2008)
An averaging principle for a completely integrable stochastic Hamiltonian system
in Nonlinearity
Xue-Mei Li (Author)
(2010)
Intertwined Diffusions by Examples