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We use a well-motivated galaxy formation framework to predict stellar masses, star formation rates (SFR), and ultraviolet (UV) luminosities of galaxy populations at redshifts $$z\in 5-16$$, taking into account stochasticity of SFR in a controlled manner. We demonstrate that the model can match observational estimates of UV luminosity functions (LFs) at $5<10$ with a modest level of SFR stochasticity, resulting in the scatter of absolute UV luminosity at a given halo mass of $$\sigma_{M_{\rm UV}}\approx 0.75$$. To match the observed UV LFs at $$z\approx 11-13$$ and $$z\approx 16$$ the SFR stochasticity should increase so that $$\sigma_{M_{\rm UV}}\approx 1-1.3$$ and $$\approx 2$$, respectively. Model galaxies at $$z\approx 11-13$$ have stellar masses and SFRs in good agreement with existing measurements. The median fraction of the baryon budget that was converted into stars, $$f_\star$$, is only $$f_\star\approx 0.005-0.05$$, but a small fraction of galaxies at $z=16$ have $$f_\star>1$$ indicating that SFR stochasticity cannot be higher. We discuss several testable consequences of the increased SFR stochasticity at $z>10$. The increase of SFR stochasticity with increasing $$z$$, for example, prevents steepening of UV LF and even results in some flattening of UV LF at $$z\gtrsim 13$$. The median stellar ages of model galaxies at $$z\approx 11-16$$ are predicted to decrease from $$\approx 20-30$$ Myr for $$M_{\rm UV}\gtrsim -21$$ galaxies to $$\approx 5-10$$ Myr for brighter ones. Likewise, the scatter in median stellar age is predicted to decrease with increasing luminosity. The scatter in the ratio of star formation rates averaged over 10 and 100 Myr should increase with redshift. Fluctuations of ionizing flux should increase at $z>10$ resulting in the increasing scatter in the line fluxes and their ratios for the lines sensitive to ionization parameter.