A decomposition of Markov processes via group actions
Probability
2014-12-30 v1
Abstract
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). We show that given a radial path, the conditioned angular part is a nonhomogeneous \levy process in a homogeneous space, we obtain a representation of such processes, and as a consequence, we extend the well known skew-product of Euclidean Brownian motion to a general setting.
Cite
@article{arxiv.1412.7843,
title = {A decomposition of Markov processes via group actions},
author = {Ming Liao},
journal= {arXiv preprint arXiv:1412.7843},
year = {2014}
}
Comments
In Theorem 4, dim(K/M) > 1 should be assumed