Fixed points and stability of neutral stochastic delay differential equations

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Abstract

In this paper we consider a linear scalar neutral stochastic differential equation with variable delays and give conditions to ensure that the zero solution is asymptotically mean square stable by means of fixed point theory. These conditions do not require the boundedness of delays, nor do they ask for a fixed sign on the coefficient functions. An asymptotic mean square stability theorem with a necessary and sufficient condition is proved. Some well-known results are improved and generalized.

Keywords

Fixed points
Stability
Neutral stochastic delay differential equations
Variable delays

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This work was partially supported by NNSF of China (Grant No. 10671043).