On geometric properties of stochastic flows related to the Lyapunov spectrum

Authors
Cranston, M
Citation
M. Cranston, On geometric properties of stochastic flows related to the Lyapunov spectrum, PROB TH REL, 118(1), 2000, pp. 1-16
Citations number
14
Categorie Soggetti
Mathematics
Journal title
PROBABILITY THEORY AND RELATED FIELDS
ISSN journal
01788051 → ACNP
Volume
118
Issue
1
Year of publication
2000
Pages
1 - 16
Database
ISI
SICI code
0178-8051(200009)118:1<1:OGPOSF>2.0.ZU;2-9
Abstract
We study the geometric properties of two stochastic flows on spheres in Euc lidean space. The underlying one-point motion in both cases is Brownian. Bo th flows arise from the action of a Lie group valued Brownian motion on a q uotient. For both flows the curvature of a curve moving under the flow is s hown to be a diffusion, null recurrent in one case and transient in the oth er.