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A stochastic version of center manifold theory
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  • Published: December 1989

A stochastic version of center manifold theory

  • Petra Boxler1 

Probability Theory and Related Fields volume 83, pages 509–545 (1989)Cite this article

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Summary

Random dynamical systems arise naturally if the influence of white or real noise on the parameters of a nonlinear determinstic dynamical system is studied. In this situation Lyapunov exponents attached to the linearized flow replace the real parts of the eigenvalues and describe the stability behavior of the linear system. If at least one of them vanishes then it is possible to prove the existence of a stochastic analogue of the deterministic center manifold. The asymptotic behavior of the entire system can then be derived from the lower dimensional system restricted to this stochastic center manifold. A dynamical characterization of the stochastic center manifold is given and approximation results are proved.

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Authors and Affiliations

  1. Institut für Dynamische Systeme, Universität Bremen, D-2800, Bremen 33, Federal Republic of Germany

    Petra Boxler

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  1. Petra Boxler
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Boxler, P. A stochastic version of center manifold theory. Probab. Th. Rel. Fields 83, 509–545 (1989). https://doi.org/10.1007/BF01845701

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  • Received: 05 February 1988

  • Revised: 10 July 1989

  • Issue Date: December 1989

  • DOI: https://doi.org/10.1007/BF01845701

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Keywords

  • Manifold
  • Dynamical System
  • Linear System
  • Asymptotic Behavior
  • Lyapunov Exponent
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