21 citations · 65 across the 7 of their papers we have counts for
7 papers
Intertwining and the Markov uniqueness problem on path spaces
K. D. Elworthy, Xue-Mei Li
There are two open problem on the analysis of continuous paths on a Riemannian manifold, the Markov uniqueness and the independence of the closure of the differential operator …
Integration by parts formulae for degenerate diffusion measures on path spaces and diffeomorphism groups
K. D. Elworthy, Yves Le Jan, Xue-Mei Li
Integration by parts formulae are given for a class of measures on the space of paths of a smooth manifold determined by the laws of degenerate diffusions. The mother of such f…
A class of integration by parts formulae in stochastic analysis I
K. D. Elworthy, Xue-Mei Li
An integration by parts formula is the foundation for stochastic analysis on path spaces over a (finite dimensional) Riemannian manifold or over , from which we may deduce the…
Special Itô maps and an Hodge theory for one forms on path spaces
K. D. Elworthy, Xue-Mei Li
We prove a Kodaira-Hodge decomposition on differential 1-forms on the space of non-smooth paths over a Riemannian manifold, allowing us to define the corresponding first cohomology…
Equivariant diffusions on Principal bundles
K. D. Elworthy, Yves Le Jan, Xue-Mei Li
Given a pair of second order diffusion operators, one on the total space of a principle bundle and the other on the base space , intertwined by the projection , if…
Some family of q-vector fields on path spaces
K. D. Elworthy, Xue-Mei Li
A great open problem is: can one learn the topology of the non-smooth path spaces with an L2 Hodge-deRham theory This one hopes to establish through a suitable complex of different…