  Assuming that the mechanism proposed by Gell-Mann and Hartle works as a
mechanism for decoherence and classicalization of the metric field, we formally
derive the form of an effective theory for the gravitational field in a
semiclassical regime. This effective theory takes the form of the usual
semiclassical theory of gravity, based on the semiclassical Einstein equation,
plus a stochastic correction which accounts for the back reaction of the lowest
order matter stress-energy fluctuations.
