Probability Theory and Related Fields

, Volume 83, Issue 4, pp 509–545 | Cite as

A stochastic version of center manifold theory

  • Petra Boxler
Article

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.

Keywords

Manifold Dynamical System Linear System Asymptotic Behavior Lyapunov Exponent 

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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Petra Boxler
    • 1
  1. 1.Institut für Dynamische SystemeUniversität BremenBremen 33Federal Republic of Germany

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