We consider a ${\mathbb{R}}^d$-valued discrete time branching random walk with a stationary and ergodic environment in time. Let $Z_n$ be the counting measure of particles of generation n. With the help of the uniform convergence of martingales and multifractal analysis, we show a large deviation result associated to the measures $Z_n$ as well as the corresponding moderate deviations.

中文翻译：

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时间随机环境中的值分支随机游动的大中度偏差

我们考虑一个 ${\mathbb{[R}}^d$时间稳定和遍历环境的高值离散时间分支随机游动。让${ž}_{ñ}$是第n代粒子的计数度量。借助of的一致收敛和多重分形分析，我们显示了与测度相关的大偏差结果${ž}_{ñ}$ 以及相应的中等偏差。