!'-!inqAFBD0 ~20332-6443 11. SUPPLEMENTARY NOTES

.3. ABSTRACT (maxim,.-In the joint work with Volker Wihstutz of the University of North Carolina, we have investigated the Lyapunov stability of systems defined by a system of differential equations with a stochastic driving term, which may be either white noise or real noise. In the first case we showed that for nilpotent systems it is possible to compute an arbitrary number of terms in the asymptotic expansion of Lyapunov exponent in fractional powers of the noise coefficient when this tends to zero. This includes the ~ ' iportant case of critically damped oscillator, which had not been treated previously. These results were then extended to the case of the same nilpotent system driven by a finite-state Markov noise process. This was obtained by a I ' method of homogenizaticn, using techniques previously established to study the central limit theorem for functions of a centered Markov chain. It was shown, as in'the case of white noise, that 'the Lyapiinc