Stochastic differential equations of Itô-type are considered and the theory of stochastic differential inequalities is systematically developed. Sufficient conditions for stability in probability, with probability one and in the mean of the Itô-type stochastic differential equations are given, using the method of cone-valued Lyapunov functions. Necessary and sufficient conditions for the construction of stochastic cone-valued Lyapunov functions are obtained for the cases where the Itô-type stochastic differential equations have uniform asymptotic stability in probability and uniform asymptotic stability in the mean. The results obtained are applied to the study of connective stability of multispecies community in a stochastic environment