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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Lévy processes in semisimple Lie groups
and stability of stochastic flows


Author: Ming Liao
Journal: Trans. Amer. Math. Soc. 350 (1998), 501-522
MSC (1991): Primary 58G32; Secondary 60H10
MathSciNet review: 1373644
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Abstract: We study the asymptotic stability of stochastic flows on compact spaces induced by Levy processes in semisimple Lie groups. It is shown that the Lyapunov exponents can be determined naturally in terms of root structure of the Lie group and there is an open subset whose complement has a positive codimension such that, after a random rotation, each of its connected components is shrunk to a single moving point exponentially under the flow.


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Additional Information

Ming Liao
Affiliation: Department of Mathematics, Auburn University, Auburn, Alabama 36849
Email: liaomin@mail.auburn.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-98-01730-9
PII: S 0002-9947(98)01730-9
Keywords: Levy processes, semisimple Lie groups, stochastic flows
Received by editor(s): June 19, 1995
Article copyright: © Copyright 1998 American Mathematical Society