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

被引：7
|
作者：
Bezborodov, Viktor [1 ]
Di Persio, Luca [1 ]
Krueger, Tyll [2 ,4 ]
Lebid, Mykola [3 ]
Ozanski, Tomasz [2 ,4 ]
机构：
[1] Univ Verona, Dept Comp Sci, Str Grazie 15, I-37134 Verona, Italy
[2] Univ Wroclaw, Wroclaw, Poland
[3] Swiss Fed Inst Technol, Dept Biosyst Sci & Engn, D BSSE, Mattenstr 26, CH-4058 Basel, Switzerland
[4] Wroclaw Univ Technol, Dept Comp Sci & Engn, Janiszewskiego 15, PL-50372 Wroclaw, Poland
来源：
ADVANCES IN APPLIED PROBABILITY | 2018年 / 50卷 / 01期
关键词：
Shape theorem; spatial birth process; growth model; 1ST-PASSAGE PERCOLATION; GROWTH; MODEL; THEOREM;
D O I：
10.1017/apr.2018.5
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
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.
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页码：74 / 101
页数：28
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