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

Pages: 332 - 342, Issue Special, September 2011

 Abstract        Full Text (337.4K)              

Nguyen Dinh Cong - Institute of Mathematics, Vietnamese Academy of Science and Technology, 18 Hoang Quoc Viet Road, 10307 Hanoi, Vietnam (email)
Nguyen Thi Thuy Quynh - Academy of Finance, Dong Ngac, Tu Liem, Hanoi, Vietnam (email)

Abstract: In this paper we show that under a nondegeneracy condition Lyapunov exponents and central exponents of linear Ito stochastic di erential 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 di erential equation which is the deterministic part of the system.

Keywords:  Lyapunov exponents, central exponents, Lyapunov spectrum, nonautonomous stochastic di erential equation, two-parameter stochastic ow
Mathematics Subject Classification:  Primary: 60H10, 37H10, 34D08; Secondary: 60G17, 34F05, 93E15

Received: July 2010;      Revised: March 2011;      Published: October 2011.