Lyapunov exponents and central exponents of linear Ito stochatic differential equations (Q540770)

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scientific article; zbMATH DE number 5903969
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Lyapunov exponents and central exponents of linear Ito stochatic differential equations
scientific article; zbMATH DE number 5903969

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    Lyapunov exponents and central exponents of linear Ito stochatic differential equations (English)
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    3 June 2011
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    From the authors' summary: ``We study Lyapunov, central and auxiliary exponents of linear Ito stochastic equations. We show that the central exponents are nonrandom like Lyapunov exponents, the non-randomness of which was proved in [\textit{Nguyen Dinh Cong}, Stoch. Dyn. 1, No.~1, 127--157 (2001; Zbl 1064.37040)]. We prove that, under a non-degeneracy condition, the central exponents \(\Theta_k\) of a linear Itô stochastic differential equation coincide with its auxiliary exponents \(\gamma_k\) and, moreover, all the first exponents coincide, i.e., \(\Theta_1 = \lambda_1 = \Omega_1 = \gamma_1\).''
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    Lyapunov exponents
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    central exponents
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    Lyapunov spectrum
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    non-autonomous stochastic differential equation
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    two-parameter stochastic flow
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