关键词: 泛函分离变量法, 随机迁移方程, 线性二阶随机常微分方程, 显式解

Abstract: In this paper，we mainly solve the generalized Wick-type stochastic transport equation in the stochastic distributions spaces (S)-1 and discuss properties of the solutions. By the sum-type functional separation of variables，the equation is reduced into a linear second-order stochastic ordinary differential equation（SODE），and then the SODE，integrated twice in order，converts to a stochastic Volterra equation，so that we obtain a class of explicit solutions in series and argue that the class of solutions are existent and unique and continuous.

Key words: functional separation of variable, stochastic transport equation, linear second-order stochastic ordinary differential equation, explicit solution