Asymptotic shape and the speed of propagation of continuous-time continuous-space birth processes

Abstract

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.

v2 update: having modified the technique, we now do not need former Condition 2.6; a proposition explicitly proving that the growth is not faster than linear is added (Proposition 3.1); some structural changes are made, as well as many minor changes, such as dealing with typos or adding details. Some of the results from arxiv.org/abs/1507.05804 are given with proofs

References in corpus (2)

• Spatial model predicts dispersal and cell turnover cause reduced intra-tumor heterogeneity
• A microscopic probabilistic description of a locally regulated population and macroscopic approximations

Cited by in corpus (4)

• Spatial growth processes with long range dispersion: microscopics, mesoscopics, and discrepancy in spread rate
• The continuous-time frog model can spread arbitrarily fast
• Spatial birth-and-death processes with a finite number of particles
• Shape theorem for a one-dimensional growing particle system with a bounded number of occupants per site