We present a theoretical formalism by which the global and the local mass functions of dark matter substructures ( dark subhalos ) can be analytically estimated .
The global subhalo mass function is defined to give the total number density of dark subhalos in the universe as a function of mass , while the local subhalo mass function counts only those subhalos included in one individual host halo .
We develop our formalism by modifying the Press-Schechter theory to incorporate the followings : ( i ) the internal structure of dark halos ; ( ii ) the correlations between the halos and the subhalos ; ( iii ) the subhalo mass-loss effect driven by the tidal forces .
We find that the resulting ( cumulative ) subhalo mass function is close to a power law with the slope of \sim - 1 , that the subhalos contribute approximately 10 \% of the total mass , and that the tidal stripping effect changes the subhalo mass function self-similarly , all consistent with recent numerical detections .