Some results of solutions to neutral stochastic functional operator-differential equations - Hu Ling; Wu Zheng; Wang Lianglong (Nonlinear Engineering)
In this article, we shall consider the solution to neutral stochastic functional operator differential equations with finite delay r>0:dD(t,xt)=f(t,xt)dt+g(t,xt)dB(t),t0≤t≤Tr\gt 0:{\rm{d}}D\left(t,{x}_{t})=f\left(t,{x}_{t}){\rm{d}}t+g\left(t,{x}_{t}){\rm{d}}B\left(t),\hspace{0.33em}{t}_{0}\le t\le T. By using Banach fixed point theorem, we obtain the existence of the solutions. We also obtain some properties of the solution.