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Acta Mathematica Vietnamica

LYAPUNOV EXPONENTS AND CENTRAL EXPONENTS OF LINEAR ITO STOCHATIC DIFFERENTIAL EQUATIONS

NGUYEN DINH CONG, NGUYEN THI THUY QUYNH

Abstract

We study Lyapunov, central and auxiliary exponents of linear Ito stochastic equations. We show that the central exponents are nonrandom like Lyapunov exponents, the nonrandomness of which was proved in [8]. We prove that under a nondegeneracy condition the central exponents $\Theta_k$ of a linear Ito stochastic differential equation coincide with its auxiliary exponents $\gamma_k$, and, moreover, all the first exponents coincide: $\Theta_1 = \lambda_1 = \Omega_1 = \gamma_1$.