In 2004 two groups have reported observation of the strong coupling regime in 3D microcavities with single quantum dots (QD). We present the quantum theory of non-linear emission of photons by such structures. We derive the exciton creation operator which coincides with a Fermi one for QDs smaller than the exciton Bohr radius and with Bose one for very large QDs. In intermediate size dots excitonic statistics is in between the Fermi and Bose ones. Consequently, the non-linear optical spectra change from the Mollow triplet in the fermionic case to the Rabi doublet in the bosonic case. We predict appearance of a characteristic multiplet structure of the non-linear emission in the intermediate regime.