Abstract
We consider finite-dimensional systems of linear stochastic differential equations ∂_{t}x_{k}(t)=A_{kp}(t)x_{p}(t), A(t) being a stationary continuous statistically isotropic stochastic process with values in real d×d matrices. We suppose that the laws of A(t) satisfy the large-deviation principle. For these systems, we find exact expressions for the Lyapunov and generalized Lyapunov exponents and show that they are determined in a precise way only by the rate function of the diagonal elements of A.
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