C_h-空间中立型随机泛函微分方程解的稳定性  

Stability of the Solution to Neutral Stochastic Functional Differential Equations with Infinite Delay at Phase Space C_h

作　　者：岳超慧[1] 张长勤[1] 

机构地区：[1]安徽农业大学理学院,安徽合肥230036

出　　处：《安徽理工大学学报（自然科学版）》2013年第2期44-47,共4页Journal of Anhui University of Science and Technology:Natural Science

基　　金：安徽省国土资源厅资助项目(2011-K-23)

摘　　要：旨在研究非Lipschitz条件下Ch-空间中具有无穷时滞的中立型随机泛函微分方程的解对初值的连续依赖性。Ch-空间不同于一般的有界连续函数空间,即BC空间;而无穷时滞的随机泛函微分方程的研究方法亦区别于有限时滞的随机泛函微分方程。因此,利用了Bihari不等式及其推论来进行稳定性的推导,结合Jensen不等式、Cauchy不等式等重要的不等式,得到了在本文的假设条件下,方程的解是均方稳定的这一结果。由此可见,在一定的条件下,将空间进行推广变化后,具有无穷时滞的中立型随机泛函微分方程仍然具备一些很好的性质。The purpose of this paper is to study the stability of the solution to neutral stochastic functional differ- ential equations with infinite delay at phase space CA under non - Lipschitz conditions on the coefficients. Phase space Ch is different from generally boundary continuous function space, which is called phase space BC; where- as, the research method of stochastic functional differential equations with infinite delay is also distinguished from stochastic functional differential equations with finite delay. In this paper, we deduce the stability by means of Bihari inequality and its corollary, Jensen inequality, Cauchy inequality and other important inequalities. Final- ly, we obtain stability in mean square of the solution to INSFDEs under the assumptions of this paper. Thus it can be seen that under certain conditions, after the generalization of the phase space, neutral stochastic function- al differential equations with infinite delay still possesses its good qualities.

关 键 词：中立型随机泛函微分方程 Ch-空间 非LIPSCHITZ条件 

分 类 号：O211[理学—概率论与数理统计]