In this paper we shall discuss the exponential stability in mean square for a neutral stochastic diierential diierence equation of the form dx(t) ? G(x(t ?))] = f(t; x(t); x(t ?))dt + (t; x(t); x(t ?))dw(t). In the case when (t; x; y) 0 this neutral stochastic diierential diierence equations becomes a deterministic neutral diierential diierence equations d dt x(t)?G(x(t?))] = f(t; x(t); x(t?))....

Abstract: The current paper is concerned with the controllability of nonlocal secondorder impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps in Hilbert spaces. Using the theory of a strongly continuous cosine family of bounded linear operators, stochastic analysis theory and with the help of the Banach fixed point theorem, we derive a ne...

Recently, we initiated in [Systems Control Lett., 26 (1995), pp. 245–251] the study of exponential stability of neutral stochastic functional differential 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 different from those used in our previous paper ...