Remarks on the existence and uniqueness of the solutions to stochastic functional differential equations with infinite delay |
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Authors: | Yong Ren Shiping Lu Ningmao Xia |
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Institution: | aDepartment of Mathematics, Anhui Normal University, Wuhu 241000, PR China;bDepartment of Mathematics, East China University of Science and Technology, Shanghai 200237, PR China |
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Abstract: | In this paper, we obtain some results on the existence and uniqueness of solutions to stochastic functional differential equations with infinite delay at phase space BC((-∞,0];Rd) which denotes the family of bounded continuous Rd-value functions defined on (-∞,0] with norm 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. |
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Keywords: | Stochastic functional differential equations Infinite delay Existence Uniqueness |
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