  In this paper, we study the existence, stability and bifurcation of random
complete and periodic solutions for stochastic parabolic equations with
multiplicative noise. We first prove the existence and uniqueness of tempered
random attractors for the stochastic equations and characterize the structures
of the attractors by random complete solutions. We then examine the existence
and stability of random complete quasi-solutions and establish the relations of
these solutions and the structures of tempered attractors. When the stochastic
equations are incorporated with periodic forcing, we obtain the existence and
stability of random periodic solutions. For the stochastic Chafee-Infante
equation, we further establish the multiplicity and stochastic bifurcation of
complete and periodic solutions.
