Coincidence of Lyapunov exponents and central exponents of linear Ito stochastic differential equations with nondegenerate stochastic term

Nguyen Dinh Cong; Nguyen Thi Thuy Quynh

doi:10.3934/proc.2011.2011.332

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2011, Volume 2011: 332-342. Doi: 10.3934/proc.2011.2011.332 open access

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Coincidence of Lyapunov exponents and central exponents of linear Ito stochastic differential equations with nondegenerate stochastic term

Nguyen Dinh Cong^1, and
Nguyen Thi Thuy Quynh^2,

1.
Institute of Mathematics, Vietnamese Academy of Science and Technology, 18 Hoang Quoc Viet Road, 10307 Hanoi
2.
Academy of Finance, Dong Ngac, Tu Liem, Hanoi

Received: June 30, 2010

Revised: February 28, 2011

Published: August 2017

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Abstract

In this paper we show that under a nondegeneracy condition Lyapunov exponents and central exponents of linear Ito stochastic dierential equation coincide. Furthermore, as the stochastic term is small and tends to zero the highest Lyapunov exponent tends to the highest central exponent of the ordinary dierential equation which is the deterministic part of the system.

Keywords:

Lyapunov exponents,
central exponents,
Lyapunov spectrum,
nonautonomous stochastic dierential equation,
two-parameter stochastic ow.

Mathematics Subject Classification: Primary: 60H10, 37H10, 34D08; Secondary: 60G17, 34F05, 93E15.

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Coincidence of Lyapunov exponents and central exponents of linear Ito stochastic differential equations with nondegenerate stochastic term

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