An open question in the field of solar and stellar astrophysics is the source of heating that causes stellar coronae to reach temperatures of millions of degrees. One possibility is that the coronae are heated by a large number of small flares. On the Sun, flares with energies as low as those of microflares are distributed with energy as a power law of the form E^-α, with α ≈ 1.8, and α appears to increase to values of 2.2-2.7 for flares of lower energy. If the slope exceeds the critical value of 2, then in principle the entire coronal energy input can be ascribed to flares that are increasingly less energetic but are more numerous. Previous analyses of flares in light curves of active stars have shown that this index generally is greater than 2, although it may be as low as 1.6 when strong flares alone are considered. Here we investigate the contribution of very weak flares, covering the milliflare energy range, to the coronal luminosity of low-mass active stars. We analyze Extreme Ultraviolet Explorer/Deep Survey events data from FK Aqr, V1054 Oph, and AD Leo and conclude that in all these cases, the coronal emission is dominated by flares to such an extent that in some cases, the entire emission can be ascribed to flare heating. We have developed a new method to directly model for the first time stochastically produced flare emission, including undetectable flares, and their effects on the observed photon arrival times. We find that α_{FK Aqr} = 2.60 ± 0.34, α_{V1054 Oph} = 2.74 ± 0.35, and α_{AD Leo} = 2.03-2.32, and the flare component accounts for a large fraction (generally greater than 50%) of the total flux.