8 citations · 8 across the 8 of their papers we have counts for
7 papers · 1 filter
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…
Convolution of probability measures on Lie groups and homogenous spaces
Ming Liao
We study (weakly) continuous convolution semigroups of probability measures on a Lie group G or a homogeneous space G/K, where K is a compact subgroup. We show that such a convolut…
A three-series theorem on Lie groups
Ming Liao
We obtain a necessary and sufficient condition for the convergence of independent products on Lie groups, as a natural extension of Kolmogorov's three-series theorem. Application t…
A decomposition of Markov processes via group actions
Ming Liao
We study a decomposition of a general Markov process in a manifold invariant under a Lie group action into a radial part (transversal to orbits) and an angular part (along an orbit…
Inhomogeneous Levy processes in Lie groups and homogeneous spaces
Ming Liao
We obtain a representation of an inhomogeneous Levy process in a Lie group or a homogeneous space in terms of a drift, a matrix function and a measure function. Because the stochas…
Isotropic self-similar Markov processes
Ming Liao, Longmin Wang
We show that an isotropic self-similar Markov process in has a skew product structure if and only if its radial and angular parts do not jump at the same time.