  We introduce a transformation of the quantum phase
$S'=S+\frac{\hbar}{2}\log\rho$, which converts the deterministic equations of
quantum mechanics into the Lagrangian reference frame of stochastic particles.
We show that the quantum potential can be removed from the transformed quantum
Hamilton-Jacobi equations if they are solved as stochastic
Hamilton-Jacobi-Bellman equations. The system of equations provide a local
description of quantum mechanics, which is enabled by the inherently
retrocausal nature of stochastic Hamilton-Jacobi-Bellman equations. We also
investigate the stochastic transformation of the classical system, where is it
shown that quantum mechanics with the quantum potential reduced by a factor of
$\frac{1}{2}$ has a classical representation, which may have interesting
implications. Finally, we discuss the notion of a subsystem correspondence
principle, which constrains the ontology of the total quantum system.
