Abstract
In this paper, we consider the long time behavior of stochastic
evolution equations. The exponential, polynomial and logarithmic decay
for stochastic equations are considered. Sufficient conditions are given
to obtain these exponents. All the results show the noise (time
diffusion) will prevent the solutions to decay in $p$-th moment, which
coincides with the fact that the noise is a diffusion process but it
will be different in the sense of almost surely, and the partial
diffusion operator (spatial diffusion) will accelerate the decay of
solutions.