Razumikhin-type exponential stability criteria of neutral stochastic functional differential equations

Janković, Svetlana; Randjelović, Jelena; Jovanović, Miljana

doi:10.1016/j.jmaa.2009.02.011

Cited by 92 publications

(33 citation statements)

References 13 publications

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“…We mention here [1,7,7] by K. Liu et al, [3,4] by S. Jankovic et al, [10] by J. Luo and [9,11,13,17] by X. Mao, for instance. However, it should be pointed out that some SDDEs are in fact stable but with respect to a certain lower decay rate which is different from exponential decay, for instance, polynomial or logarithmic one.…”

Section: Dx(t) = [Ax(t) + Bx(t − τ )] Dt + [Cx(t) + Dx(t − τ )] Dw(t)mentioning

confidence: 99%

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Moment decay rates of stochastic differential equations with time-varying delay

Janković

Pavlović

2010

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One of the most important questions, especially in applications, is how to choose a decay function in the study of stability for a concrete equation. Motivated by the fact that the coefficients of the considered equation mainly suggest the choice of the decay function, the point of analysis in the paper is to carry out the Lyapunov function approach and to state coercivity conditions dependent on decay in the study of the pth moment stability with a general decay rate for a certain stochastic differential equation with variable time delay. Some criteria including the usual exponential decay are discussed, particularly the ones with a concave decay, special cases of which are polynomial and logarithmic decays. Some consequences and examples are given to illustrate the theory.

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Section: Dx(t) = [Ax(t) + Bx(t − τ )] Dt + [Cx(t) + Dx(t − τ )] Dw(t)mentioning

confidence: 99%

“…Motivated by papers [3,4,16], for p ≥ 2 we can state a more effective and relatively easy way to verify criteria, in fact the consequences of Theorems 1-4, by taking particularly V (x, t) ≡ |x| p . Then, in view of (4),…”

Section: Some Consequences and Examplesmentioning

confidence: 99%

Moment decay rates of stochastic differential equations with time-varying delay

Janković

Pavlović

2010

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“…It is well-known that there is significant and very rich literature discussing special techniques to study almost sure and pth mean exponential stability of solutions to various classes of stochastic differential equations (see monographs [12] and [15] by X. Mao, and [6,9,11,19], for instance). However, less attention has been devoted to asymptotic stability of Itô-Volterra integrodifferential equations (see [1,2,3,13,14] and literature cited therein, among other things).…”

Section: X(t) = F (T X(t)) + G T X(t)mentioning

confidence: 99%

Pth mean asymptotic stability and integrability of Itô-Volterra integrodifferential equations

Janković

Obradović

2009

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“…One of the basic works of the theory of neutral functional differential equations is to study the theory of stability of solutions. Moreover, there is an extensive literature on the stability of neutral stochastic functional differential equations (NSFDEs), such as [2,3,12,15,[18][19][20][21]28]. In particular, Mao [19] investigated the exponential stability in mean square for a NSFDEs.…”

Section: Introductionmentioning

confidence: 99%