JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (05): 82-87.doi: 10.6040/j.issn.1671-9352.0.2014.237

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Stability of neutral stochastic differential equations with some variable delays

WANG Chun-sheng1, LI Yong-ming2   

  1. 1. South China Institute of Software Engineering, Guangzhou University, Guangzhou 510990, Guangdong, China;
    2. Shangrao Normal University, Shangrao 334001, Jiangxi, China
  • Received:2014-05-23 Online:2015-05-20 Published:2015-05-29

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Abstract: We consider a class of linear scalar neutral stochastic differential equation with some variable delays and give conditions to ensure that the zero solution is asymptotically stable in mean square by means of Banach fixed point method. Previously, when almost all the experts and scholars study the stability of stochastic differential equations by means of Banach fixed point, it is usually achieved and accomplished by introducing appropriate functions. Being different from most other study methods, we will split the introduced functions when studying the stability of stochastic differential equations with some variable delays to construct the operator in this paper. Then, study its stability by ways of Banach fixed point, promote and improve the previous studies. Also an example was given to illustrate the results in the paper.

Key words: Banach fixed points, neutral stochastic differential equations,some variable delays, asymptotically stable in mean square

CLC Number: 

  • O211.63
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