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Lyapunov exponents of nilpotent Itô systems with random coefficients

Author

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  • Baxendale, Peter H.
  • Goukasian, Levon

Abstract

The paper considers the top Lyapunov exponent of a two-dimensional linear stochastic differential equation. The matrix coefficients are assumed to be functions of an independent recurrent Markov process, and the system is a small perturbation of a nilpotent system. The main result gives the asymptotic behavior of the top Lyapunov exponent as the perturbation parameter tends to zero. This generalizes a result of Pinsky and Wihstutz for the constant coefficient case.

Suggested Citation

  • Baxendale, Peter H. & Goukasian, Levon, 2001. "Lyapunov exponents of nilpotent Itô systems with random coefficients," Stochastic Processes and their Applications, Elsevier, vol. 95(2), pages 219-233, October.
    • Handle: RePEc:eee:spapps:v:95:y:2001:i:2:p:219-233
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    Cited by:

    1. Sowers, Richard B., 2009. "Averaging of stochastic flows: Twist maps and escape from resonance," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3549-3582, October.

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