The stochastic scheme proposed in a previous paper as subjacent to quantum mechanics is analyzed in the light of the difficulties and criticisms encountered by similar attempts. It is shown that the limitation of the domain where the theory is valid gives a reply to the criticisms, but restricts its practical usefulness to the description of basic features. A stochastic approach of the hadron mass spectrum, allowing the scheme to emerge in the domain of experimental verification (to be worked out (...) in a later paper) is outlined. The model is found not to be in disagreement with Bell's argument opposed to hidden variables; a same origin is suggested for the difficulties encountered in both domains. The views proposed are compared with the Copenhagen interpretation: common points and divergences are analyzed. (shrink)