In this paper, using the stochastic modeling of the non-equilibrium statistical mechanics in the momentum space, the evolution equations of the parton distribution functions (PDF ) usually used in the hadrons phenomenology are generated. These stochastic modeling PDF evolution equations are the same as those of the Dokshitzer–Gribov– Lipatov–Altarelli–Parisi (DGLAP) ones, but they can be obtained by a more simplistic mathematical procedure based on the non-equilibrium statistical mechanics and the theory of Markov processes.
