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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Received: 30 April 1999 / Revised version: 4 October 1999 / Published online: 8 August 2000
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Cranston, M. On geometric properties of stochastic flows related to the Lyapunov spectrum. Probab Theory Relat Fields 118, 1–16 (2000). https://doi.org/10.1007/PL00008737
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DOI: https://doi.org/10.1007/PL00008737
Keywords
- Brownian Motion
- Lyapunov Exponent
- Geometric Property
- Fundamental Form
- Quadratic Variation