So far there are not many results on the stability for stochastic functional differential equations with infinite delay. Themain aim of this paper is to establish some new criteria on the stability with general decay rate for stochastic functional differential equations with infinite delay. To illustrate the applications of our theories clearly, this paper also examines a scalar infinite delay ...

During the last few years, a number of articles has been appeared in the literature, which are motivated by the old but very interesting papers by Driver [7, 8] and Driver, Sasser and Slater [10] dealing with the asymptotic behavior and the stability of the solutions of delay differential equations. See [2, 4, 5, 12, 13, 17-21, 27-41, 44]. These articles are concerned with the asymptotic behavi...

In this article, we study the existence and asymptotic stability in pth moment of mild solutions to second order neutral stochastic partial differential equations with delay. Our method of investigating the stability of solutions is based on fixed point theorem and Lipchitz conditions being imposed.

In this paper, the approximate controllability of fractional impulsive neutral stochastic differential equations with nonlocal conditions and infinite delay in Hilbert spaces is studied. By using the Krasnoselskii-Schaefer-type fixed point theorem and stochastic analysis theory, some sufficient conditions are given for the approximate controllability of the system. At the end, an example is giv...