309 citations · 392 across the 15 of their papers we have counts for
15 papers
Formulae for the derivatives of heat semigroups
K. D. Elworthy, Xue-Mei Li
We use a basic martingale method to show a differentiation formula for the derivatives The…
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 …
Geometric stochastic analysis on path spaces
K. D. Elworthy, Xue-Mei Li
An approach to analysis on path spaces of Riemannian manifolds is described. The spaces are furnished with `Brownian motion' measure which lies on continuous paths, though differen…
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…
Concerning the geometry of stochastic differential equations and stochastic flows
K. D. Elworthy, Y. LeJan, Xue-Mei Li
Following Le Jan and Watanabe we define a connection associated with a non-degenrrate diffusion operators. This connection is characterized here and shown to be the Levi-Civita con…
The vanishing of L2 harmonic one-forms on based path spaces
K. D. Elworthy, Y. Yang
We prove the triviality of the first L2 cohomology class of based path spaces of Riemannian manifolds furnished with Brownian motion measure, and the consequent vanishing of L2 har…
The Geometry of Filtering
K. D. Elworthy, Y. LeJan, Xue-Mei Li
Geometry arising from two diffusion operators (smooth semi-elliptic, second order differential operators) on different spaces but intertwined by a smooth map is described. Particul…
Ito maps and analysis on path spaces
K. D. Elworthy, Xue-Mei Li
We consider versions of Malliavin calculus on path spaces of compact manifolds with diffusion measures, defining Gross-Sobolev spaces of differentiable functions and proving their…
Generalized Ito Formulae and Space-Time Lebesgue-Stieltjes Integrals of Local Times
K. D. Elworthy, A. Truman, H. Z. Zhao
Generalised Ito formulae are proved for time dependent functions of continuous real valued semi-martingales. The conditions involve left space and time first derivatives, with the…
Bounded and Harmonic Forms on Universal Covers
K. D. Elworthy, Xue-Mei Li, Steven Rosenberg
We relate the positivity of the curvature term in the Weitzenbock formula for the Laplacian on p-forms on a complete manifold to the existence of bounded and harmonic forms.…
Homotopy and Homology Vanishing Theorems and the Stability of Stochastic Flows
K. D. Elworthy, Steven Rosenberg
We relate stability properties (i.e. moment exponents) of a stochastic dynamical system on a compact manifold to the homotopy and integral homology groups of . In the specia…