Assuming that the space-time consists of elementary domains proposed by Yukawa, we attempt to extend the stochastic quantization procedures introduced by Nelson in the non-relativistic case to the relativistic one. In our view, the conventional Minkowski structure of space-time is to reflect the macroscopic property, so that it may be derived from our stochastic formulation as its continuum limit. The relativistic wave equation is set up to describe the behavior of successive inter-elementary-domain transitions of an excitation. It is found that the equation is of the Fock-Nambu-Feynman type.