连续时间连续空间生灭过程的渐近形状与传播速度
概率论
2018-04-13 v2
摘要
我们在某些一般条件下，针对连续时间连续空间随机生长模型阐述并证明了一个形状定理。与经典格点生长模型类似，该证明利用了次可加遍历定理。在截断自由分支出生率的情况下，给出了传播速度的精确表达式。
引用
@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}
}
备注
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