Stochastic processes of a quantum state

Starting from a quantum state represented by its wave function (x), satisfying the Schrödinger equation, we determine stochastic processes which provide the same time evolution for the probability density(x)=¦(x)¦². The transition probabilities of these processes are explicitly built in two circumstances: in the general case, but in an expansion in the time difference, and exactly, but for Gaussian processes. This allows us to discuss the correspondence between quantum states and stochastic processes, which appears not to be one-to-one, but, on the contrary, to associate with the same state an infinity of processes which differ in the fluctuation correlations of the random variable.