Existence, uniqueness and stability of the solutions to neutral stochastic functional differential equations with infinite delay

In this paper, we obtain the existence and uniqueness of solutions to neutral 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 φ defined on ( - ∞ , 0 ] with norm ‖ φ ‖ = sup -...

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Veröffentlicht in:Applied mathematics and computation Jg. 210; H. 1; S. 72 - 79
Hauptverfasser: Ren, Yong, Xia, Ningmao
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier Inc 01.04.2009
Elsevier
Schlagworte:
Calculus of variations and optimal control
Exact sciences and technology
Infinite delay
Mathematical analysis
Mathematics
Neutral stochastic functional differential equations
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Picard approximation
Real functions
Sciences and techniques of general use
Neutral stochastic functional differential equations
Picard approximation
Infinite delay
Differential equation
Existence of solution
Continuous function
Neutral stochastic functional differential
equations
Successive approximation
Numerical analysis
Neutral equation
Applied mathematics
Integral equation
Numerical stability
Stochastic equation
ISSN:0096-3003, 1873-5649
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Zusammenfassung:In this paper, we obtain the existence and uniqueness of solutions to neutral 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 φ defined on ( - ∞ , 0 ] with norm ‖ φ ‖ = sup - ∞ < θ ⩽ 0 | φ ( θ ) | 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. Furthermore, we give the continuous dependence of solutions on the initial value by means of the Corollary of Bihari inequality.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2008.11.009