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A covariant generalization of a non-relativistic stochastic quantum mechanicsintroduced by de la Pe\~na and Cetto is formulated. The analysis is done inspace-time and avoids the use of a non-covariant time evolution parameter inorder to search for Lorentz invariance. The covariant form of the set ofiterative equations for the joint coordinate and momentum distribution function$Q(x,p)$ is derived and expanded in power series of the charge of the particle.Then, solutions of the zeroth order in the charge of the iterative equationsfor $Q(x,p)$ are considered. For them, it follows that the space-timeprobability density $\rho(x)$ and the function $S(x)$ which gradient definesthe mean value of the momentum at the space time point $x$, define a complexfunction $\psi(x)$ which exactly satisfies the Klein-Gordon (KG) equation. Itis argued that when the KG solution is either of positive or negative energy,the total number of particles conserves in the random motion. It follows thatthe total number of particles conserves when $\psi(x)$ composed alternativelyof pure positive or negative energy modes. In addition, solutions for the jointdistribution function in lowest order, satisfying the positive condition arealso found. They suggests a possible link with the Couder's experiments ondroplet movements over oscillating liquid surfaces.

A relativistic formulation of the de la Pe\~na-Cetto stochastic quantum mechanics