  The time-dependent cosmological term arises from the energy-momentum tensor
calculated in a state different from the ground state. We discuss the
expectation value of the energy-momentum tensor on the rhs of Einstein
equations in various (approximate)pure as well as mixed states. We apply the
classical slow-roll field evolution as well as the Starobinsky and warm
inflation stochastic equations in order to calculate the expectation value. We
show that in a state concentrated at the local maximum of the double-well
potential the expectation value is decreasing exponentially. We confirm the
descend of the expectation value in the stochastic inflation model. We
calculate the cosmological constant $\Lambda$ at large time as the expectation
value of the energy density with respect to the stationary probability
distribution. We show that $\Lambda\simeq \gamma^{\frac{4}{3}} where $\gamma$
is the thermal dissipation rate.
