A Decomposition of Markov Processes via Group Actions

Ming Liao ()
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Ming Liao: Auburn University

Journal of Theoretical Probability, 2009, vol. 22, issue 1, 164-185

Abstract: 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 Lévy 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.

Keywords: Markov processes; Lévy processes; Lie groups; Homogeneous spaces; 60J25; 58J65 (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/s10959-008-0162-x

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