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Razumikhin-type theorems on general decay stability of stochastic functional differential equations with infinite delay. (English) Zbl 1247.34128

By the Razumikhin-type technique, this paper examines the general decay stability of stochastic functional differential equations with infinite delay. This result extends Mao’s work [X. Mao, Stochastic differential equation and applications. 2nd ed. Chichester: Horwood Publishing (2007; Zbl 1138.60005)] to the general decay stability and infinite delay. This paper also applies this result to examine the general decay stability of stochastic delay differential equations with infinite delay and distributed delay.
Reviewer: Fuke Wu (Wuhan)

MSC:

34K50 Stochastic functional-differential equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34K20 Stability theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations

Citations:

Zbl 1138.60005
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References:

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