Quantum mechanics from stochastic processes

We construct an explicit one-to-one correspondence between non-relativistic stochastic processes and solutions of the Schrödinger equation and between relativistic stochastic processes and solutions of the Klein–Gordon equation. The existence of this equivalence suggests that the Lorentzian path integral can be defined as an Itô integral, similar to the definition of the Euclidean path integral in terms of the Wiener integral. Moreover, the result implies a stochastic interpretation of quantum theories.