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Decomposition of stochastic flows and Lyapunov exponents
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  • Published: August 2000

Decomposition of stochastic flows and Lyapunov exponents

  • Ming Liao1 

Probability Theory and Related Fields volume 117, pages 589–607 (2000)Cite this article

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Abstract.

Let φ t be the stochastic flow of a stochastic differential equation on a compact Riemannian manifold M. Fix a point m∈M and an orthonormal frame u at m, we will show that there is a unique decomposition φ t = ξ t ψ t such that ξ t is isometric, ψ t fixes m and Dψ t (u) = us t , where s t is an upper triangular matrix. We will also establish some convergence properties in connection with the Lyapunov exponents and the decomposition Dφ t (u) = u t s t with u t being an orthonormal frame. As an application, we can show that ψt preserves the directions in which the tangent vectors at m are dilated at fixed exponential rates.

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Authors and Affiliations

  1. Department of Mathematics, Auburn University, 208 Parker Hall, Auburn, AL 36849, USA. e-mail: liaomin@mail.auburn.edu. , , , , , , US

    Ming Liao

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  1. Ming Liao
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Received: 19 November 1998 / Revised version: 1 October 1999 / Published online: 14 June 2000

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Liao, M. Decomposition of stochastic flows and Lyapunov exponents. Probab Theory Relat Fields 117, 589–607 (2000). https://doi.org/10.1007/PL00008736

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  • Issue Date: August 2000

  • DOI: https://doi.org/10.1007/PL00008736

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  • Mathematics Subject Classfication (1991): Primary 58G32; Secondary 60H10
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