  In this paper, we investigate the existence and uniqueness of weak pullback
mean random attractors for abstract stochastic evolution equations with general
diffusion terms in Bochner spaces. As applications, the existence and
uniqueness of weak pullback mean random attractors for some stochastic models
such as stochastic reaction-diffusion equations, the stochastic $p$-Laplace
equation and stochastic porous media equations are established.
