  In this note, we generalize the asymptotic shape theorem proved in [Des14a]
for a class of random growth models whose growth is at least and at most
linear. In this way, we obtain asymptotic shape theorems conjectured for
several models: the contact process in a randomly evolving environment [SW08],
the oriented percolation with hostile immigration [GM12b] and the bounded
modified contact process [DS00].

Probability