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

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2022. Vol. 105. No. 5. Article 9.
Il'in A. S., Копьев А., Сирота В. А., Zybin K.

We consider finite-dimensional systems of linear stochastic differential equations ∂txk(t)=Akp(t)xp(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.

Research target: Mathematics
Language: English
DOI
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Keywords: турбулентностьстохастические дифференциальные уравненияlinear stochastic differential equationLarge deviations theorymulticomponent stochastic systemsСлучайные матрицыproduct of random matricesмультипликативный интегралвероятность и стохастический анализtheory of turbulence
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