Perturbation methods for Lyapunov exponents

In order to investigate the long term behavior of a linear dynamical system under the impact of multiplicative mean zero noise, the top Lyapunov exponent associated with the system is studied with its dependence upon the noise intensity and other parameters of the (mostly 2-dimensional) systems. The perturbation methods, most singular, are surveyed systematically, which yield (a) asymptotic expansions of the Lyapunov exponents in terms of small and large intensities of different kinds of noise; (b) a comparison of white and real noise and (c) a characterization of stabilizing noise.