Remarks on the existence and uniqueness of the solutions to stochastic functional differential equations with infinite delay
By Yong Ren, Shiping Lu, N. Xia. 2008
66 citations recorded by the source corpus.
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];R^d) which denotes the family of bounded continuous R^d-value functions @f defined on (-~,0] with norm @?@f@?=sup"-"~"<"@q"=<"0|@f(@q)| 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.
Subfields: Applied Mathematics, Control and Systems Engineering, Finance
View Paper: https://www.semanticscholar.org/paper/b3c694214759d78dd8cc0f4fdf3f232bf66cddad
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In Applied Mathematics
In Control and Systems Engineering
In Finance
Citations in the corpus
- Stochastic functional differential equations with infinite delay driven by G‐Brownian motion (2013, methodology): “[4] generalized the existence and uniqueness of solutions to ISFDEs under non-Lipschitz condition with Lipschitz condition being considered as a special case, and the solution is constructed by the successive approximation.”
- Existence, Uniqueness and Stability Results of Impulsive Stochastic Semilinear Neutral Functional Differential Equations with Infinite Delays (2009, unknown): “Motivated by [13; 14], we generalize the existence and uniqueness of the solution to impulsive stochastic partial neutral functional differential equations (ISNFDEs) under non-Lipschitz conditions and under Lipschitz conditions.”