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.
@article{1177005582,
author = {Pinsky, Mark A.},
title = {Extremal Character of the Lyapunov Exponent of the Stochastic Harmonic Oscillator},
journal = {Ann. Appl. Probab.},
volume = {2},
number = {4},
year = {1992},
pages = { 942-950},
language = {en},
url = {http://dml.mathdoc.fr/item/1177005582}
}
Pinsky, Mark A. Extremal Character of the Lyapunov Exponent of the Stochastic Harmonic Oscillator. Ann. Appl. Probab., Tome 2 (1992) no. 4, pp. 942-950. http://gdmltest.u-ga.fr/item/1177005582/