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Differential Equations with Random Delay

  • S. Siegmund
  • T. S. Doan
Chapter
Part of the Fields Institute Communications book series (FIC, volume 64)

Abstract

The Multiplicative Ergodic Theorem by Oseledets on Lyapunov spectrum and Oseledets subspaces is extended to linear random differential equations with random delay, using a recent result by Lian and Lu. Random differential equations with bounded delay are discussed as an example.

Notes

Acknowledgements

The authors were supported in part by DFG Emmy Noether Grant Si801/1-3.

Received 4/16/2009; Accepted 2/14/2010

References

  1. [1].
    L. Arnold, Random Dynamical Systems (Springer, Berlin, 1998)CrossRefGoogle Scholar
  2. [2].
    H. Crauel, T.S. Doan, S. Siegmund, Difference equations with random delay. J. Differ. Equat. Appl. 15, 627–647 (2009)MathSciNetCrossRefGoogle Scholar
  3. [3].
    J.K. Hale, J. Kato, Phase space for retarded equations with infinite delay. Funkcial. Ekvac. 21, 11–41 (1978)Google Scholar
  4. [4].
    Y. Hino, S. Murakami, T. Naito, Functional Differential Equations with Infinite Delay. Lecture Notes in Mathematics, vol. 1473 (Springer, Berlin, 1991)Google Scholar
  5. [5].
    Z. Lian, K. Lu, Lyapunov exponents and invariant manifolds for random dynamical systems in a Banach space. Memoirs of the American Mathematical Society. 206 (2010)MathSciNetCrossRefGoogle Scholar
  6. [6].
    D. Ruelle, Ergodic theory of differentiable dynamical systems. Inst. Hautes Études Sci. Publ. Math. 50, 27–58 (1979)MathSciNetCrossRefGoogle Scholar
  7. [7].
    S. Willard, General Topology (Addison-Wesley, Reading, 1970)Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsImperial College LondonLondonUK
  2. 2.Institute of MathematicsVietnam Academy of Science and TechnologyHa NoiViet Nam

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