Open Access
April, 1992 Symmetry Groups of Markov Processes
Ming Liao
Ann. Probab. 20(2): 563-578 (April, 1992). DOI: 10.1214/aop/1176989791


We prove that if $G$ is a subgroup of the (time-change) symmetry group of a Markov process $X_t$ which is transitive and has a compact isotropy subgroup, then after a time change, $X_t$ becomes $G$-invariant. The symmetry groups of diffusion processes are discussed in more detail. We show that if the generator of $X_t$ is the Laplacian with respect to the intrinsic metric, then $X_t$ has the best invariance property.


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Ming Liao. "Symmetry Groups of Markov Processes." Ann. Probab. 20 (2) 563 - 578, April, 1992.


Published: April, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0755.60061
MathSciNet: MR1159559
Digital Object Identifier: 10.1214/aop/1176989791

Primary: 60J45
Secondary: 58G32

Keywords: Diffusion processes , invariance groups , invariant processes , Markov processes , Riemannian metrics and Laplacians , symmetry groups

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.20 • No. 2 • April, 1992
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