The Random Walk in Generalized Quantum Theory
  One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we ``quantize'' the classical random walk by finding, subject to a certain condition of ``strong positivity'', the most general Markovian, translationally invariant ``decoherence functional'' with nearest neighbor transitions. 
Xavier Martin, Denjoe O'Connor, and R.D. Sorkin