Asymptotic shape and the speed of propagation of continuous-time continuous-space birth processes
Probability
2018-04-13 v2
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.
Keywords
Cite
@article{arxiv.1609.04070,
title = {Asymptotic shape and the speed of propagation of continuous-time continuous-space birth processes},
author = {Viktor Bezborodov and Luca Di Persio and Tyll Krueger and Mykola Lebid and Tomasz Ożański},
journal= {arXiv preprint arXiv:1609.04070},
year = {2018}
}
Comments
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