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

作者：Luo; Jiaowan

来源：Journal of Computational and Applied Mathematics, 2007, 198(1): 143-148.

DOI：10.1016/j.cam.2005.11.019

• exponential stability
• stochastic delay differential equations
• stochastic difference equations
• Euler-Maruyama scheme

In a very recent paper, Baker and Buckwar [Exponential stability in pth mean of solutions, and of convergent Euter-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.

• 出版日期2007-1-1
• 单位广州大学