Probability Theory and Related Fields

, Volume 118, Issue 1, pp 1–16 | Cite as

On geometric properties of stochastic flows related to the Lyapunov spectrum

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Abstract

We study the geometric properties of two stochastic flows on spheres in Euclidean space. The underlying one-point motion in both cases is Brownian. Both flows arise from the action of a Lie group valued Brownian motion on a quotient. For both flows the curvature of a curve moving under the flow is shown to be a diffusion, null recurrent in one case and transient in the other.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of RochesterRochesterUSA

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