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.
Asymptotic shape and the speed of propagation of continuous-time continuous-space birth processes
Bezborodov V.;Di Persio L.
;
2018
Abstract
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.
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Descrizione: This is a pre-final revision of the paper. The article can be found here: https://www.cambridge.org/core/journals/advances-in-applied-probability/article/asymptotic-shape-and-the-speed-of-propagation-of-continuoustime-continuousspace-birth-processes/3232E000771D08A0CF2A9566970A137C
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