The existence and uniqueness of the solution for stochastic functional differential equations with infinite delay |
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Authors: | Fengying Wei Ke Wang |
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Institution: | a College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350002, PR China b Department of Mathematics, Harbin Institute of Technology, Weihai 264209, PR China |
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Abstract: | This paper is devoted to build the existence-and-uniqueness theorem of solutions to stochastic functional differential equations with infinite delay (short for ISFDEs) at phase space BC((−∞,0];Rd). Under the uniform Lipschitz condition, the linear growth condition is weaked to obtain the moment estimate of the solution for ISFDEs. Furthermore, the existence-and-uniqueness theorem of the solution for ISFDEs is derived, and the estimate for the error between approximate solution and accurate solution is given. On the other hand, under the linear growth condition, the uniform Lipschitz condition is replaced by the local Lipschitz condition, the existence-and-uniqueness theorem is also valid for ISFDEs on t0,T]. Moreover, the existence-and-uniqueness theorem still holds on interval t0,∞), where t0∈R is an arbitrary real number. |
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Keywords: | Stochastic functional differential equations Infinite delay Existence Uniqueness |
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