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http://dx.doi.org/10.4134/JKMS.2012.49.3.515

ON THE GENERAL DECAY STABILITY OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY  

Meng, Xuejing (Department of Statistics and Mathematics Hubei University of Economics)
Yin, Baojian (School of Mathematics and Statistics Huazhong University of Science and Technology)
Publication Information
Journal of the Korean Mathematical Society / v.49, no.3, 2012 , pp. 515-536 More about this Journal
Abstract
This work focuses on the general decay stability of nonlinear stochastic differential equations with unbounded delay. A Razumikhin-type theorem is first established to obtain the moment stability but without almost sure stability. Then an improved edition is presented to derive not only the moment stability but also the almost sure stability, while existing 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.
Keywords
stochastic delay differential equation; unbounded delay; Razumikhin-type theorem; stability; M-matrix;
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