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

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.

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

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.