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Remarks on the existence and uniqueness of the solutions to stochastic functional differential equations with infinite delay. (English) Zbl 1152.34388

Summary: We obtain some results on the existence and uniqueness of solutions to stochastic functional differential equations with infinite delay at phase space BC((\(-\infty ,0]; \mathbb R^d\)) which denotes the family of bounded continuous \(\mathbb R^d\)-value functions \(\varphi\) defined on (\(-\infty ,0\)] with norm \(\| \varphi \| = \sup _{-\infty <\theta \leqslant 0}|\varphi(\theta)|\) 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.

MSC:

34K50 Stochastic functional-differential equations
34K07 Theoretical approximation of solutions to functional-differential equations
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References:

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