We consider the stochastic quantization method for scalar fields defined in a
curved manifold and also in a flat space-time with event horizon. The two-point
function associated to a massive self-interacting scalar field is evaluated, up
to the first order level in the coupling constant, for the case of an Einstein
and also a Rindler Euclidean metric, respectively. Its value for the asymptotic
limit of the Markov parameter is exhibited. The divergences therein are taken
care of by employing a covariant stochastic regularization