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Zbl 1166.60040
Janković, Svetlana; Randjelović, Jelena; Jovanović, Miljana
Razumikhin-type exponential stability criteria of neutral stochastic functional differential equations. (English)
[J] J. Math. Anal. Appl. 355, No. 2, 811-820 (2009). ISSN 0022-247X

Summary: The paper discusses both $p$th moment and almost sure exponential stability of solutions to neutral stochastic functional differential equations and neutral stochastic differential delay equations, by using the Razumikhin-type technique. The main goal is to find sufficient stability conditions that could be verified more easily then by using the usual method with Lyapunov functionals. The analysis is based on a paper of {\it X. Mao} [SIAM J. Math. Anal. 28, No.~2, 389--401 (1997; Zbl 0876.60047)], referring to mean square and almost sure exponential stability.

MSC 2000:: *60H20 Stochastic integral equations
34K50 Stochastic delay equations

Keywords: Brownian motion; neutral stochastic functional differential equation; Razumikhin-type theorems; $p$th moment exponential stability; almost sure exponential stability

Citations: Zbl 0876.60047

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