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On the general decay stability of stochastic differential equations with unbounded delay

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This work focuses on the general decay stability of nonlinear stochastic differential equations with unbounded delay. A Razumikhin-type theorem is rst established to obtain the moment stability but with-out almost sure stability. Then an improved edition is presented to derive not only the moment stability but also the almost sure stability, while ex-isting Razumikhin-type theorems aim at only the moment stability. By virtue of the M-matrix techniques, we further develop the aforementioned Razumikhin-type theorems to be easily implementable. Two examples are given for illustration.

Abstract

This work focuses on the general decay stability of nonlinear stochastic differential equations with unbounded delay. A Razumikhin-type theorem is rst established to obtain the moment stability but with-out almost sure stability. Then an improved edition is presented to derive not only the moment stability but also the almost sure stability, while ex-isting Razumikhin-type theorems aim at only the moment stability. By virtue of the M-matrix techniques, we further develop the aforementioned Razumikhin-type theorems to be easily implementable. Two examples are given for illustration.

참고문헌 (24)

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