Existence-uniqueness and continuation theorems for stochastic functional differential equations |
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Authors: | Daoyi Xu Yumei Huang |
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Affiliation: | a Yangtze Center of Mathematics, Sichuan University, Chengdu 610064, PR China b College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, PR China |
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Abstract: | The main aim of this paper is to develop some basic theories of stochastic functional differential equations (SFDEs). Firstly, we establish stochastic versions of the well-known Picard local existence-uniqueness theorem given by Driver and continuation theorems given by Hale and Driver for functional differential equations (FDEs). Then, we extend the global existence-uniqueness theorems of Wintner for ordinary differential equations (ODEs), Driver for FDEs and Taniguchi for stochastic ordinary differential equations (SODEs) to SFDEs. These show clearly the power of our new results. |
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Keywords: | Stochastic functional differential equations Existence Uniqueness Continuation theorem |
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