Asymptotic shape and the speed of propagation of continuous-time   continuous-space birth processes
  We formulate and prove a shape theorem for a continuous-time continuous-space stochastic growth model under certain general conditions. Similarly to the classical lattice growth models the proof makes use of the subadditive ergodic theorem. A precise expression for the speed of propagation is given in the case of a truncated free branching birth rate. 
Viktor Bezborodov, Luca Di Persio, Tyll Krueger, Mykola Lebid, Tomasz   O\.za\'nski
math.PR