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

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