Variations on the Langevin equation for lattice QCD with fermions

The purpose of this Brief Report is to present new versions of a recently proposed Langevin process for the simulation of lattice QCD. These include Runge-Kutta algorithms that lead to accuracy of O(${\epsilon }^2$), instead of O(ε). We also mention the possible use of a new simple Euler algorithm to give O(${\epsilon }^2$) errors in renormalized physical quantities.