Journals / Turkish Journal of Mathematics / 2010 / Cilt: 34 - Sayı: 1
Existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay in Lp(W,Ch)
- Pages
- 45–58
- DOI
- —
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.
Özet
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.