A note on exponential stability in pth mean of solutions of stochastic delay differential equations

Authors:
Jiaowan Luo
Affiliations:
School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, Guangdong, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 1
Cited 2

Exponential stability in p-th mean of solutions, and of convergent Euler-type solutions, of stochastic delay differential equations

Journal of Computational and Applied Mathematics

Dynamic Analysis of Stochastic Recurrent Neural Networks

Neural Processing Letters
Mean-square stability of semi-implicit Euler method for nonlinear neutral stochastic delay differential equations

Applied Numerical Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

In a very recent paper, Baker and Buckwar [Exponential stability in pth mean of solutions, and of convergent Euler-type solutions, of stochastic delay differential equations, J. Comput. Appl. Math. 184 (2005) 404-427] investigated the exponential stability in pth mean of solutions of stochastic delay differential equations with multiplicative noise, and of stochastic difference equations which are Euler-Maruyama discretization of stochastic delay differential equations. The Dini derivative of the expectation of V(t, X(t)) "along" X(t) is taken in their stability analysis. Unfortunately, the main results derived by them are somewhat restrictive to be applied for practical purposes. In this note we shall improve the corresponding results. An example is given to illustrate our theory.