# Gaussian fluctuations and a law of the iterated logarithm for Nerman’s martingale in the supercritical general branching process

@article{Iksanov2020GaussianFA,
title={Gaussian fluctuations and a law of the iterated logarithm for Nerman’s martingale in the supercritical general branching process},
author={Alexander Iksanov and Konrad Kolesko and Matthias Meiners},
journal={Electronic Journal of Probability},
year={2020}
}
• Published 11 May 2020
• Mathematics
• Electronic Journal of Probability
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…
2 Citations

### Публікації викладачів кафедри

2. Я.М. Чабанюк, А.В. Нікітін, У.Т. Хімка. Асимптотичні властивості еволюційних систем з марковськими переключеннями з використанням апроксимаційних схем. Wydawnictwo Politechniki Lubelskiej, Lublin,

### Asymptotic fluctuations in supercritical Crump-Mode-Jagers processes

• Mathematics
• 2021
Abstract. Consider a supercritical Crump–Mode–Jagers process (Z t )t≥0 counted with random characteristic φ. Nerman’s celebrated law of large numbers [Z. Wahrsch. Verw. Gebiete 57, 365–395, 1981]

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