Some central limit analogues for supercritical Galton-Watson processes
Some central limit analogues for supercritical Galton-Watson processes
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DOI：
10.2307/3211837
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发表时间：
1971-03
影响因子：
1
通讯作者：
C. Heyde
中科院分区：
文献类型：
--
作者：
C. Heyde
可以将独立随机变量和的经典中心极限定理解释为大数定律的收敛速度结果。例如，如果Xi，i = 1，2，3，···是独立同分布的随机变量，其中EXi = μ，var Xi = σ2 < ∞，那么中心极限定理可以写成这样的形式这提供了关于收敛速度的信息强定律为。（“a.s.”）表示几乎必然收敛。）本文的目的是讨论超临界Galton-Watson过程的类似物。
It is possible to interpret the classical central limit theorem for sums of independent random variables as a convergence rate result for the law of large numbers. For example, if Xi, i = 1, 2, 3, ··· are independent and identically distributed random variables with EXi = μ, var Xi = σ2 < ∞ and then the central limit theorem can be written in the form This provides information on the rate of convergence in the strong law as . (“a.s.” denotes almost sure convergence.) It is our object in this paper to discuss analogues for the super-critical Galton-Watson process.