  In this paper, we investigate the existence and stability of random
transition fronts of KPP-type lattice equations in random media, and explore
the influence of the media and randomness on the wave profiles and wave speeds
of such solutions. We first establish comparison principle for sub-solutions
and super-solutions of KPP type lattice random equations and prove the
stability of positive constant equilibrium solution. Next, by constructing
appropriate sub-solutions and super-solutions, we show the existence of random
transition fronts. Finally, we prove the stability of random transition fronts
of KPP-type lattice random equations.
