We study the process of four-wave mixing (FWM) in ultracold degenerate atom
ic gases. In particular, we address the problem of FWM in boson-fermion mix
tures. We develop an approximate description of such processes using asympt
otic analysis of high-order perturbation theory taking into account quantum
statistics. We perform also numerical simulations of FWM in boson-fermion
mixtures and obtain an analytic and numerical estimate of the efficiency of
the process.