Electron. J. Diff. Equ., Vol. 2009(2009), No. 143, pp. 1-10.

Boundedness and exponential stability of highly nonlinear stochastic differential equations

Ruihua Liu, Youssef Raffoul

Abstract:
In this article we consider nonlinear stochastic differential systems and use Lyapunov functions to study the boundedness and exponential asymptotic stability of solutions. We provide several examples in which we consider stochastic systems with unbounded terms.

Submitted October 30, 2008. Published November 12, 2009.
Math Subject Classifications: 34F05, 60H10.
Key Words: Boundedness; exponential stability; Lyapunov function; stochastic differential equation.

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Ruihua Liu
Department of Mathematics, University of Dayton
300 College Park, Dayton, OH 45469, USA
email: ruihua.liu@notes.udayton.edu
Youssef Raffoul
Department of Mathematics, University of Dayton
300 College Park, Dayton, OH 45469, USA
email: youssef.raffoul@notes.udayton.edu

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