Abstract
Let A be a G-invariant differential operator on a homogeneous space M = G/H, which is the generator of some diffusion process. We study the existence of a G-valued stochastic flow whose one point motion is an A- diffusion in terms of the Lie algebra of G. When M is a Riemannian symmetric space, we show that there exists an isometric stochastic flow whose one point motion is a Brownian motion if M is a symmetric space of compact type and such a flow does not exist if M is of non-compact type. The uniqueness of such a flow is also discussed.
Research supported by the Huo Ying Dong Educational Fundation and NSF of RR. China.
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Liao, M. (1992). The Existence of Isometric Stochastic Flows for Riemannian Brownian Motions. In: Pinsky, M.A., Wihstutz, V. (eds) Diffusion Processes and Related Problems in Analysis, Volume II. Progress in Probability, vol 27. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0389-6_4
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DOI: https://doi.org/10.1007/978-1-4612-0389-6_4
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6739-3
Online ISBN: 978-1-4612-0389-6
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