Turkish Journal

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Mathematics

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# Turkish Journal of Mathematics

Existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay in Lp(W,Ch)

Haibo BAO
Department of Mathematics and Physics,
Hohai University, Nanjing,
210098, Jiangsu-CHINA
e-mail: hbbao@hhu.edu.cn

Abstract: In this paper, we shall consider the existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay in Lp(W,Ch) space: d[x(t)-G(xt)]=f(t,xt)dt+g(t,xt)dB(t), where we assume f:R+\times Lp(W,Ch) \to Lp(W,Rn), g:R+\times Lp(W,Ch) \to Lp(W,L(Rm, Rn)), G: Lp(W,Ch) \to Lp(W,Rn), p>2,\, and B(t) is a given m-dimensional Brownian motion.

Key Words: Neutral stochastic functional differential equations; existence; uniqueness; infinite delay.

Turk. J. Math., 34, (2010), 45-58.
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Other articles published in the same issue: Turk. J. Math.,vol.34,iss.1.