Long-term properties of finite-correlation time isotropic stochastic systems

Abstract

We consider finite-dimensional systems of linear stochastic differential equations ${\partial }_t{x}_k\left(t\right)=A_{kp}\left(t\right)x_p\left(t\right)$, $\mathbf{A}(t)$ being a stationary continuous statistically isotropic stochastic process with values in real $d\times d$ matrices. We suppose also that the laws of $\mathbf{A}(t)$ 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 $\mathbf{A}$.

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Cited by in corpus (6)

• Suppression of small-scale dynamo in time irreversible turbulence
• Relative efficiency of three mechanisms of vector fields growth in a random media
• Magnetic energy spectrum produced by turbulent dynamo: effect of time irreversibility
• Lagrangian stochastic integrals of motion in isotropic random flows
• Material surfaces in stochastic flows: integrals of motion and intermittency
• Small-scale turbulent dynamo for low-Prandtl number fluid: comparison of the theory with results of numerical simulations