论文标题
迭代的对数定律，用于迭代随机步行，并应用于随机递归树木
A law of the iterated logarithm for iterated random walks, with application to random recursive trees
论文作者
论文摘要
考虑一个越来越多的随机步行产生的crump模式 - 震撼过程，该过程的增量是有限的第二刻。令$ y_k（t）$为$ k \ in \ mathbb n $中的个人数量，以时间间隔$ [0，t] $。我们证明了$ y_k（t）$的迭代对数法律，带有固定的$ k $，为$ t \ to +\ to +\ infty $。结果，我们在随机递归树中的固定水平$ k $以迭代对数的定律得出了一项法律，因为顶点数量为$ \ infty $。
Consider a Crump-Mode-Jagers process generated by an increasing random walk whose increments have finite second moment. Let $Y_k(t)$ be the number of individuals in generation $k\in \mathbb N$ born in the time interval $[0,t]$. We prove a law of the iterated logarithm for $Y_k(t)$ with fixed $k$, as $t\to +\infty$. As a consequence, we derive a law of the iterated logarithm for the number of vertices at a fixed level $k$ in a random recursive tree, as the number of vertices goes to $\infty$.
