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We aim at developing a robust methodology for constraining the luminosity andstellar mass functions (LMFs) of galaxies by solely using data frommulti-filter surveys and testing the potential of these techniques fordetermining the evolution of the miniJPAS LMFs up to $z\sim0.7$. Stellar massand $B$-band luminosity for each of the miniJPAS galaxies are constrained usingan updated version of the SED-fitting code MUFFIT, whose values are based oncomposite stellar population models and the probability distribution functionsof the miniJPAS photometric redshifts. Galaxies are classified through thestellar mass versus rest-frame colour diagram corrected for extinction.Different stellar mass and luminosity completeness limits are set andparametrised as a function of redshift, for setting limits in our flux-limitedsample ($r_\mathrm{SDSS}<22$). The miniJPAS LMFs are parametrised according toSchechter-like functions via a novel maximum likelihood method accounting foruncertainties, degeneracies, probabilities, completeness, and priors. Overall,our results point to a smooth evolution with redshift ($0.05<z<0.7$) of theminiJPAS LMFs in agreement with previous work. The LMF evolution ofstar-forming galaxies mainly involve the bright and massive ends of thesefunctions, whereas the LMFs of quiescent galaxies also exhibit a non-negligibleevolution on their faint and less massive ends. The cosmic evolution of theglobal $B$-band luminosity density decreases ~0.1 dex from $z=0.7$ to 0,whereas for quiescent galaxies this quantity roughly remains constant. Incontrast, the stellar mass density increases ~0.3 dex at the same redshiftrange, where such evolution is mainly driven by quiescent galaxies owing to anoverall increasing number of this kind of galaxies, which in turn includes themajority and most massive galaxies (60-100% fraction of galaxies at$\log_{10}(M_\star/M_\odot)>10.7$).

The miniJPAS survey. Evolution of the luminosity and stellar mass functions of galaxies up to $z \sim 0.7$