  We present precision Monte Carlo calculations solving the QCD evolution
equations up to the next-to-leading-order (NLO) level. They employ forward
Markovian Monte Carlo (FMC) algorithms, which provide the rigorous solutions of
the QCD evolution equations. Appropriate Monte Carlo algorithms are described
in detail. They are implemented in the form of the Monte Carlo program EvolFMC,
which features the NLO kernels for the QCD evolution. The presented numerical
results agree with those from independent, non-MC, programs (QCDNum16,
APCheb33) at the level of 0.1%. In this way we have demonstrated the
feasibility of the precision MC calculations for the QCD evolution and provided
very useful numerical tests (benchmarks) for other, non-Markovian, MC
algorithms developed recently.
