Rigorous derivation of Born’s rule in the colored-noise model

Establish a rigorous derivation of Born’s rule for the stochastic quantum-field-theoretic model in which the fermion density operator is coupled to the Lorentz-invariant colored noise field h(x).

Background

The paper refers to an earlier model in which the fermion density operator is coupled to a colored noise field h(x), obtained by solving a d’Alembert equation with white noise as the source. Although that model yields exponentially decaying spatial correlations and an analytically calculable correlation length, the probabilistic interpretation required by quantum theory has not been rigorously established.

The unresolved issue is specifically whether the model can derive Born’s rule rather than merely reproduce stochastic wave-function dynamics.