Recently, we generated the evolution equations of the parton distribution functions (PDF) usually used in the hadrons phenomenology by the stochastic modeling of the non-equilibrium statistical mechanics in the momentum space. The evolution equations obtained from the stochastic modeling are the same as the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations, but they are acquired by a mathematical procedure based on the non-equilibrium statistical mechanics and Markov processes. In this paper, we present a new analytical solution of the parton evolution equation (DGLAP equation) for the non-singlet quark distribution function using the generating function method. This method is a general technique for solving the master equation of Markov processes.
