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Asymptotic mean square stability analysis for a stochastic delay differential equation

For a stochastic delay differential equation, the effects of noise and time delay are discussed in the sense of mean square stability. Neither time delay nor noise play bad roles for the differential equations and both of them are ubiquitous in nature. The so-called domain subdivision approach is taken to study the stability regions in terms of the parameters of a given equation and the Ito formula is employed to deal with the fluctuation noise. An interesting result demonstrated in this paper shows that noise with appropriate power could reduce the influence of time delay.