  For linear stochastic differential equations (SDEs) with bounded
coefficients, we establish the robustness of nonuniform mean-square exponential
dichotomy (NMS-ED) on $[t_{0},+\oo)$, $(-\oo,t_{0}]$ and the whole $\R$
separately, in the sense that such an NMS-ED persists under a sufficiently
small linear perturbation. The result for the nonuniform mean-square
exponential contraction (NMS-EC) is also discussed.
  Moreover, in the process of proving the existence of NMS-ED, we use the
observation that the projections of the "exponential growing solutions" and the
"exponential decaying solutions" on $[t_{0},+\oo)$, $(-\oo,t_{0}]$ and $\R$ are
different but related. Thus, the relations of three types of projections on
$[t_{0},+\oo)$, $(-\oo,t_{0}]$ and $\R$ are discussed.
