Razumikhin-type theorems on general decay stability of stochastic functional differential equations with infinite delay

Authors:
Gorica Pavlović;Svetlana Janković
Affiliations:
-;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

Citing 4
Cited 1

Razumikhin-type theorems on exponential stability of neutral stochastic functinal differential equations

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Brief paper: Robustness of exponential stability of a class of stochastic functional differential equations with infinite delay

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Abstract

To the best of the authors' knowledge, there are no results based on the so-called Razumikhin technique via a general decay stability, for any type of stochastic differential equations. In the present paper, the Razumikhin approach is applied to the study of both pth moment and almost sure stability on a general decay for stochastic functional differential equations with infinite delay. The obtained results are extended to stochastic differential equations with infinite delay and distributed infinite delay. Some comments on how the considered approach could be extended to stochastic functional differential equations with finite delay are also given. An example is presented to illustrate the usefulness of the theory.