2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69607We consider the time-inhomogeneous Markovian jump process introduced by John S. Bell [Phys.Rep. 137, 49] for a lattice quantum field theory, which runs on the associated configuration space. Its jump rates, tailored to give the process the quantum distribution $|Ψ_t|^2$ at all times $t$, typically exhibit singularities. We establish the existence of a unique such process for all times, under suitable assumptions on the Hamiltonian or the initial state vector $Ψ_0$. The proof of non-explosion takes advantage of the special role of the $|Ψ_t|^2$ distribution.16 pages LaTeX, no figures; v2: references added, minor extension of the introductionProbabilityMathematical PhysicsQuantum Physics60J75; 81T25text