论文标题
在随机环境中移民的分支随机步行的中央限制定理和浆果 - 贝里界的界限
Central limit theorem and Berry-Esseen bounds for a branching random walk with immigration in a random environment
论文作者
论文摘要
我们考虑在$ d $维的真实空间上进行分支随机步行，并在时间依赖的随机环境中移民。令$ z_n（\ mathbf t）$为该过程的所谓分区功能，即，在描述了时间$ n $的计数量度的时刻生成计数措施的函数。对于$ \ mathbf t $固定的，对数$ \ log z_n（\ mathbf t）$满足中心限制定理。通过研究系统的内在字体及其收敛速率的对数力矩，我们建立了与中心极限定理相对应的均匀和非均匀的浆果 - 贝里 - 埃斯式界限，并发现中心极限定理中的确切收敛速率。
We consider a branching random walk on $d$-dimensional real space with immigration in a time-dependent random environment. Let $Z_n(\mathbf t)$ be the so-called partition function of the process, namely, the moment generating function of the counting measure describing the dispersion of individuals at time $n$. For $\mathbf t$ fixed, the logarithm $\log Z_n(\mathbf t)$ satisfies a central limit theorem. By studying the logarithmic moments of the intrinsic submartingale of the system and its convergence rates, we establish the uniform and non-uniform Berry-Esseen bounds corresponding to the central limit theorem, and discover the exact convergence rate in the central limit theorem.
