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On geometric properties of stochastic flows related to the Lyapunov spectrum
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  • Published: 12 February 2014

On geometric properties of stochastic flows related to the Lyapunov spectrum

  • M. Cranston1 

Probability Theory and Related Fields volume 118, pages 1–16 (2000)Cite this article

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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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Authors and Affiliations

  1. Department of Mathematics, University of Rochester, Rochester, NY 14627, USA. e-mail: cran@math.rochester.edu, USA

    M. Cranston

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  1. M. Cranston
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Received: 30 April 1999 / Revised version: 4 October 1999 / Published online: 8 August 2000

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Cite this article

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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  • Published: 12 February 2014

  • Issue Date: September 2000

  • DOI: https://doi.org/10.1007/PL00008737

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Keywords

  • Brownian Motion
  • Lyapunov Exponent
  • Geometric Property
  • Fundamental Form
  • Quadratic Variation
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