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Extremal character of the Lyapunov exponent of the stochastic harmonic oscillator. (English) Zbl 0788.60072
Author’s abstract: We give a formula for the quadratic Lyapunov exponent of the harmonic oscillator in the presence of a finite-state Markov process. In case the noise process is reversible, the quadratic Lyapunov exponent is strictly less than that for the corresponding white-noise process obtained from the central limit theorem. An example is presented of a nonreversible Markov process for which this inequality is reversed.
Reviewer: J.H.Kim (Pusan)

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34D05 Asymptotic properties of solutions to ordinary differential equations
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