We first provide some sufficient conditions for the existence of
global compact random attractors for general random dynamical systems in
weighted space l^p_/rho ( p /geq 1) of infinite sequences.  We then
consider the existence of global compact random attractors in weighted
space l^2_/rho for stochastic lattice dynamical systems with random
coupled coefficients and multiplicative/additive white noise.   The
results recover many existing ones on the existence of global random
attractors for stochastic latice dynamical systems with
multiplicative/additive white noises in regular l^2 space of infinite
sequences.