A Decomposition of Markov Processes via Group Actions |
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Authors: | Ming Liao |
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Affiliation: | (1) Department of Mathematics, Auburn University, Auburn, AL 36849, USA |
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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. |
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Keywords: | Markov processes Lévy processes Lie groups Homogeneous spaces |
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