  A wave front of Fisher and Kolmogorov, Petrovskii, and Piskunov type
involving two species A and B with different diffusion coefficients $D_A$ and
$D_B$ is studied using a master equation approach in dilute and concentrated
solutions. Species A and B are supposed to be engaged in the autocatalytic
reaction A+B -> 2A. Contrary to the results of a deterministic description, the
front speed deduced from the master equation in the dilute case sensitively
depends on the diffusion coefficient of species B. A linear analysis of the
deterministic equations with a cutoff in the reactive term cannot explain the
decrease of the front speed observed for $D_B > D_A$. In the case of a
concentrated solution, the transition rates associated with cross-diffusion are
derived from the corresponding diffusion fluxes. The properties of the wave
front obtained in the dilute case remain valid but are mitigated by
cross-diffusion which reduces the impact of different diffusion coefficients.
