论文标题
高斯的波动和在超批评一般分支机构中，纽曼的马丁那的迭代对数定律
Gaussian fluctuations and a law of the iterated logarithm for Nerman's martingale in the supercritical general branching process
论文作者
论文摘要
在他的1981年开始的古典作品中，Nerman广泛使用了关键的Martingale $（w_t）_ {t \ geq 0} $，以证明概率的概率，几乎肯定地肯定地，肯定地肯定地证明了具有一般特征的超级策略通用分支过程（又称Crump-Mode-Jagigers Branching Processes）。 Martingale终端价值$ W $数字在其结果的范围内。 我们调查了Martingale（现在称为Nerman的Martingale）的利率，其汇聚为限制$ W $。更准确地说，假设存在Malthusian参数$α> 0 $和$ W_0 \在L^2 $中，我们证明了$（W-W_ {T+S}）_ {s {S \ in \ Mathbb {r}} $的功能性中心限制定理，如弱极限是随机缩放时间变化的布朗运动。在其他技术假设下，我们证明了$ w-w_t $的迭代对数法律。
In his, by now, classical work from 1981, Nerman made extensive use of a crucial martingale $(W_t)_{t \geq 0}$ to prove convergence in probability, in mean and almost surely, of supercritical general branching processes (a.k.a. Crump-Mode-Jagers branching processes) counted with a general characteristic. The martingale terminal value $W$ figures in the limits of his results. We investigate the rate at which the martingale, now called Nerman's martingale, converges to its limit $W$. More precisely, assuming the existence of a Malthusian parameter $α> 0$ and $W_0\in L^2$, we prove a functional central limit theorem for $(W-W_{t+s})_{s\in\mathbb{R}}$, properly normalized, as $t\to\infty$. The weak limit is a randomly scaled time-changed Brownian motion. Under an additional technical assumption, we prove a law of the iterated logarithm for $W-W_t$.
