关键词: 无穷时滞, 中立型随机偏泛函微分方程, 适度解, 存在唯一性

Abstract: Firstly，the definition of the mild solution to neutral stochastic partial functional differential equations with infinite delay in Hilbert spaces was introduced. Then，by means of the properties of analytic semigroups， Burkholder-Davis-Gundy inequality， and Banach fixed point theorem，the existence and uniqueness of the mild solution to neutral stochastic partial functional differential equations with infinite delay in Hilbert spaces were obtained. Finally，an example was given to illustrate the results.

Key words: infinite delay, neutral stochastic partial functional differential equations, mild solution, existence and uniqueness