Electron. J. Diff. Equ., Vol. 2015 (2015), No. 285, pp. 1-23.

Exponential P-stability of stochastic nabla-dynamic equations on disconnected sets

Huu Du Nguyen, Thanh Dieu Nguyen, Anh Tuan Le

The aim of this article is to consider the existence of solutions, finiteness of moments, and exponential p-stability of stochastic $\nabla$-dynamic equations on an arbitrary closed subset of $\mathbb{R}$, via Lyapunov functions. This work can be considered as a unification and generalization of works dealing with random difference and stochastic differential equations.

Submitted April 4, 2013. Published November 11, 2015.
Math Subject Classifications: 60H10, 34A40, 34D20, 39A13, 34N05.
Key Words: Differential operator; dynamic equation; exponential stability; Ito's formula; Lyapunov function.

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Huu Du Nguyen
Faculty of Mathematics, Mechanics, and Informatics
University of Science-VNU
334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam
email: dunh@vnu.edu.vn
Thanh Dieu Nguyen
Department of Mathematics, Vinh University
182 Le Duan, Vinh, Nghe An, Vietnam
email: dieunguyen2008@gmail.com
Anh Tuan Le
Faculty of Fundamental Science
Hanoi University of Industry
Tu Liem district, Ha Noi, Vietnam
email: tuansl83@yahoo.com

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