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.

引用

页码：74 / 101

页数：28

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