Stochastic interpretation of quantum mechanics

We express the probabilistic character associated to the wave function by treating it as a stochastic variable. This is accomplished by means of a stochastic equation for the wave function whose noise changes the phase of the wave function but not its absolute value, so that the norm of the wave function is strictly conserved along a stochastic trajectory. We show that the density matrix that obeys the quantum Liouville equation is the covariance matrix associated to the stochastic wave function.