ASYMPTOTIC SHAPE AND THE SPEED OF PROPAGATION OF CONTINUOUS-TIME CONTINUOUS-SPACE BIRTH PROCESSES

作者:Bezborodov Viktor*; Di Persio Luca; Krueger Tyll; Lebid Mykola; Ozanski Tomasz
来源:Advances in Applied Probability, 2018, 50(1): 74-101.
DOI:10.1017/apr.2018.5

摘要

We formulate and prove a shape theorem for a continuous-time continuous-space stochastic growth model under certain general conditions. Similar 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.

  • 出版日期2018-3