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The idea of obtaining a pilot-wave quantum theory on a lattice with discretetime is presented. The motion of quantum particles is described by a$|\Psi|^2$-distributed Markov chain. Stochastic matrices of the process arefound by the discrete version of the least-action principle. Probabilitycurrents are the consequence of Hamilton's principle and the stochasticity ofthe Markov process is minimized. As an example, stochastic motion of singleparticles in a double-slit experiment is examined.

Pilot-wave quantum theory in discrete space and time and the principle of least action