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arXiv 1609.04070math.PR
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连续时间连续空间出生过程的渐近形状和传播速度

Asymptotic shape and the speed of propagation of continuous-time continuous-space birth processes

Viktor Bezborodov, Luca Di Persio, Tyll Krueger, Mykola Lebid, Tomasz Ożański

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
发表信息：
Advances in Applied Probability, 50(1), 74-101, 2018
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摘要：

在一定的一般条件下，给出并证明了连续时间连续空间随机增长模型的形状定理。类似于经典的晶格生长模型的证明利用次加性遍历定理。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。

英文摘要：

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

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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