We give a formula for the quadratic Lyapunov exponent of the harmonic oscillator in the presence of a finite-state Markov noise 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 noise process for which this inequality is reversed.
"Extremal Character of the Lyapunov Exponent of the Stochastic Harmonic Oscillator." Ann. Appl. Probab. 2 (4) 942 - 950, November, 1992. https://doi.org/10.1214/aoap/1177005582