Fixed points and stability of neutral stochastic delay differential equations |
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Authors: | Jiaowan Luo |
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Institution: | Department of Probability and Statistics, School of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong 510006, PR China |
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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. |
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Keywords: | Fixed points Stability Neutral stochastic delay differential equations Variable delays |
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