Existence, uniqueness and stability of the solutions to neutral stochastic functional differential equations with infinite delay
Existence, uniqueness and stability of the solutions to neutral stochastic functional differential equations with infinite delay
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DOI：
10.1016/j.amc.2008.11.009
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发表时间：
2009-04
期刊：
影响因子：
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通讯作者：
Yong Ren;N. Xia
中科院分区：
文献类型：
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作者：
Yong Ren;N. Xia
本文得到了在相空间BC((-∞,0)；Rd上具有无限延迟的中立型随机泛函微分方程解的存在唯一性，该方程表示在（-∞,0）上定义的有界连续Rd值函数族φ，范数‖φ‖=sup-∞<θ < 0|φ(θ)|，在非Lipschitz条件下，将Lipschitz条件视为一种特殊情况和一种弱线性增长条件。解是由逐次逼近构造的。进一步，利用Bihari不等式的推论，给出了解对初值的连续依赖关系。
In this paper, we obtain the existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay at phase space BC((-∞,0];Rd) which denotes the family of bounded continuous Rd- value functions φ defined on (-∞,0] with norm ‖φ‖=sup-∞<θ⩽0|φ(θ)| under non-Lipschitz condition with Lipschitz condition being considered as a special case and a weakened linear growth condition. The solution is constructed by the successive approximation. Furthermore, we give the continuous dependence of solutions on the initial value by means of the Corollary of Bihari inequality.