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

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