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We consider the stochastic quantization method for scalar fields defined in acurved manifold and also in a flat space-time with event horizon. The two-pointfunction associated to a massive self-interacting scalar field is evaluated, upto the first order level in the coupling constant, for the case of an Einsteinand also a Rindler Euclidean metric, respectively. Its value for the asymptoticlimit of the Markov parameter is exhibited. The divergences therein are takencare of by employing a covariant stochastic regularization.

Stochastic Quantization of Scalar Fields in Einstein and Rindler Spacetime