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Random perturbation to the geodesic equation

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Title: Random perturbation to the geodesic equation
Authors: Li, X-M
Item Type: Journal Article
Abstract: We study random “perturbation” to the geodesic equation. The geodesic equation is identified with a canonical differential equation on the orthonormal frame bundle driven by a horizontal vector field of norm 11. We prove that the projections of the solutions to the perturbed equations, converge, after suitable rescaling, to a Brownian motion scaled by 8n(n−1)8n(n−1) where nn is the dimension of the state space. Their horizontal lifts to the orthonormal frame bundle converge also, to a scaled horizontal Brownian motion.
Issue Date: 2-Feb-2016
Date of Acceptance: 1-Oct-2014
URI: http://hdl.handle.net/10044/1/54116
DOI: https://dx.doi.org/10.1214/14-AOP981
ISSN: 0091-1798
Publisher: Institute of Mathematical Statistics
Start Page: 544
End Page: 566
Journal / Book Title: Annals of Probability
Volume: 44
Copyright Statement: © Institute of Mathematical Statistics, 2016
Keywords: Science & Technology
Physical Sciences
Statistics & Probability
Mathematics
Horizontal flows
horizontal Brownian motions
vertical perturbation
stochastic differential equations
homogenisation
geodesics
CENTRAL-LIMIT-THEOREM
FLOWS
DIFFUSIONS
math.PR
0104 Statistics
Notes: mrclass: 60H10 (37Hxx 53B05 58J65) mrnumber: 3456345 mrreviewer: Dejun Luo
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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