Ruzumikhin-type theorems on exponential stability of stochastic functional differential equations (1996) [2 citations — 2 self]
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Abstract:
Abstract. Recently, we initiated in [Systems Control Lett., 26 (1995), pp. 245--251] the study of exponential stability of neutral stochastic functional di#erential equations, and in this paper, we shall further our study in this area. We should emphasize that the main technique employed in this paper is the well-known Razumikhin argument and is completely di#erent from those used in our previous paper [Systems Control Lett., 26 (1995), pp. 245--251]. The results obtained in [Systems Control Lett., 26 (1995), pp. 245--251] can only be applied to a certain class of neutral stochastic functional di#erential equations excluding neutral stochastic di#erential delay equations, but the results obtained in this paper are more general, and they especially can be used to deal with neutral stochastic di#erential delay equations. Moreover, in [Systems Control Lett., 26 (1995), pp. 245--251], we only studied the exponential stability in mean square, but in this paper, we shall also study the almost sure exponential stability. It should be pointed out that although the results established in this paper are applicable to more general neutral-type equation, for a particular type of equation discussed in [Systems Control Lett., 26 (1995), pp. 245--251], the results there are sharper.
