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Remarks on the existence and uniqueness of the solutions to stochastic functional differential equations with infinite delay

โœ Scribed by Yong Ren; Shiping Lu; Ningmao Xia

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
151 KB
Volume
220
Category
Article
ISSN
0377-0427

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โœฆ Synopsis

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((-โˆž, 0]; R d ) which denotes the family of bounded continuous R d -value functions defined on (-โˆž, 0] with norm = sup -โˆž< 0 | ( )| 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.

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In this paper we shall consider the existence, uniqueness, and asymptotic behavior of mild solutions to stochastic partial functional differential equations with finite delay r > 0: dX(t)=[ -AX(t)+f(t, X t )] dt+g(t, X t ) dW(t), where we assume that -A is a closed, densely defined linear operator a