41 citations · 71 across the 19 of their papers we have counts for
22 papers
Markov Processes with Jumps on Manifolds and Lie Groups
David Applebaum, Ming Liao
We review some developments concerning Markov and Feller processes with jumps in geometric settings. These include stochastic differential equations in Markus canonical form, the C…
Properties of Lévy Generators on Compact Riemannian Manifolds
David Applebaum, Rosemary Shewell Brockway
We consider isotropic Lévy processes on a compact Riemannian manifold, obtained from an -valued Lévy process through rolling without slipping. We prove that the Felle…
On the Spectrum of Self--Adjoint Lévy Generators
David Applebaum
We investigate the spectrum of the generator of a self-adjoint transition semigroup of a (symmetric) Lévy process taking values in --dimensional space.
The Positive Maximum Principle on Symmetric Spaces
David Applebaum, Trang Le Ngan
We investigate the Courrège theorem in the context of linear operators that satisfy the positive maximum principle on a space of continuous functions over a symmetric space. Ap…
The Positive Maximum Principle on Lie Groups
David Applebaum, Trang Le Ngan
We extend a classical theorem of Courrège to Lie groups in a global setting, thus characterising all linear operators on the space of smooth functions of compact support that satis…
Transition Densities and Traces for Invariant Feller Processes on Compact Symmetric Spaces
David Applebaum, Trang Le Ngan
We find necessary and sufficient conditions for a finite -bi-invariant measure on a compact Gelfand pair to have a square-integrable density. For convolution semigroups…