Exponential stability for stochastic neutral partial functional differential equations

Abstract

In this paper, we consider a class of stochastic neutral partial functional differential equations in a real separable Hilbert space. Some conditions on the existence and uniqueness of a mild solution of this class of equations and also the exponential stability of the moments of a mild solution as well as its sample paths are obtained. The known results in Govindan [T.E. Govindan, Almost sure exponential stability for stochastic neutral partial functional differential equations, Stochastics 77 (2005) 139–154], Liu and Truman [K. Liu, A. Truman, A note on almost sure exponential stability for stochastic partial functional differential equations, Statist. Probab. Lett. 50 (2000) 273–278] and Taniguchi [T. Taniguchi, Almost sure exponential stability for stochastic partial functional differential equations, Stoch. Anal. Appl. 16 (1998) 965–975; T. Taniguchi, Asymptotic stability theorems of semilinear stochastic evolution equations in Hilbert spaces, Stochastics 53 (1995) 41–52] are generalized and improved.