41 citations · 71 across the 19 of their papers we have counts for
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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.
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…
Convolution Semigroups of Probability Measures on Gelfand Pairs, Revisited
David Applebaum
Our goal is to find classes of convolution semigroups on Lie groups that give rise to interesting processes in symmetric spaces . The -bi-invariant convolution semigrou…
Probabilistic Trace and Poisson Summation Formulae on Locally Compact Abelian Groups
David Applebaum
We investigate convolution semigroups of probability measures with continuous densities on locally compact abelian groups, which have a discrete subgroup such that the factor group…