Lower estimations for the Lyapunov exponents of linear systems of differential equations perturbed by white noise (Q1388211)

Let \[ \dot x=A(t)x, \quad t\in R,\;x\in R^n, \tag{1} \] be a linear system of differential equations and let \[ dy= A(t)ydt+ \sigma\sum^m_{k=1} B_kyd\xi_k(t), \tag{2} \] where \(\xi_k (t)\) are mutually independent standard Wiener processes and \(\sigma\) is a positive parameter, be its random perturbation. The problem of the behavior of the Lyapunov exponents of system (2) is studied. The author obtains a lower estimation for Lyapunov exponents of (2) by a kind of central exponents of the deterministic system (1) for small parameter \(\sigma\).