Li, X-M. (2016) Random perturbation to the geodesic equation. The Annals of Probability, 44 (1). pp. 544-566. doi:10.1214/14-AOP981 ISSN 0091-1798.

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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 . We prove that the projections of the solutions to the perturbed equations, converge, after suitable rescaling, to a Brownian motion scaled by [Math Processing Error] where [Math Processing Error] is the dimension of the state space. Their horizontal lifts to the orthonormal frame bundle converge also, to a scaled horizontal Brownian motion.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Geodesics (Mathematics), Perturbation (Mathematics)
Journal or Publication Title:	The Annals of Probability
Publisher:	Institute of Mathematical Statistics
ISSN:	0091-1798
Official Date:	2 February 2016
Dates:	Date Event 2 February 2016 Published 2015 Accepted August 2014 Submitted
Volume:	44
Number:	1
Number of Pages:	23
Page Range:	pp. 544-566
DOI:	10.1214/14-AOP981
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	3 June 2016
Date of first compliant Open Access:	6 June 2016
Funder:	Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	EP/E058124/1 (EPSRC)
Adapted As:

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