We investigate the contribution of very weak flares to the coronal luminosity of low-mass active stars. We analyze EUVE/DS 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 may 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 the index of the power-law distribution of flare energies (dN/dE ~ E^{-alpha}) is 2.6+-0.34, 2.74+-0.35, and 2.03-2.32 for FK Aqr, V1054 Oph, and AD Leo respectively. We also find that the flare component accounts for a large fraction (generally >50 percent) of the total flux.

20 pages in 2-columns AASTeX, 12 figures, accepted for publication in ApJ