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تسجيل مستخدم جديدRobustness of nonuniform mean-square exponential dichotomies
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Hailong Zhu
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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.
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