[en] The aim of the experiment is to create the quantum stochastic process in a curved space-time for the simpliest case of a neutral scalar field. A general scheme of quantum accidental processes is given. A covariant determination of a stochastic integral is introduced. A generalized formula of Eta and covariant equations of Kolmogorov-Klein-Fock are obtained. Wave functions are presented as quantum expectations and as contour integrals. It is pointed out that the formalism may be applied to the construction of a general covariant theory of classical accidental processes in the Rieman space