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Asymptotic behaviour of stochastic flows of diffeomorphisms: Two case studies
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  • Published: March 1986

Asymptotic behaviour of stochastic flows of diffeomorphisms: Two case studies

  • Peter H. Baxendale1 

Probability Theory and Related Fields volume 73, pages 51–85 (1986)Cite this article

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Summary

The two stochastic flows studied are (i) the canonical stochastic flow on the orthonormal frame bundle of hyperbolic space (which gives stochastic parallel translation along Brownian paths in hyperbolic space) and (ii) a stochastic flow on the sphereS n-1 arising from its embedding as the unit sphere in ℝn. Both flows are controlled by the same stochastic differential equation in a finite-dimensional Lie group. In each case the Lyapunov exponents are computed and a complete description is given of the local and global stability of the flow.

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Authors and Affiliations

  1. Department of Mathematics, University of Aberdeen, AB9 2TY, Aberdeen, Scotland, U.K.

    Peter H. Baxendale

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  1. Peter H. Baxendale
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Baxendale, P.H. Asymptotic behaviour of stochastic flows of diffeomorphisms: Two case studies. Probab. Th. Rel. Fields 73, 51–85 (1986). https://doi.org/10.1007/BF01845993

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  • Received: 09 September 1984

  • Revised: 28 February 1986

  • Issue Date: March 1986

  • DOI: https://doi.org/10.1007/BF01845993

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Keywords

  • Differential Equation
  • Stochastic Process
  • Asymptotic Behaviour
  • Probability Theory
  • Lyapunov Exponent
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