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Павлов Ю.Л.
О скорости сходимости к нормальному закону распределений числа деревьев заданного объема в лесе Гальтона – Ватсона
// Труды КарНЦ РАН. No 6. Сер. Математическое моделирование и информационные технологии. 2026. C. 82-88
Pavlov Yu.L. On the rate of normal approximation for the distribution of the number of trees of a given size in a Galton – Watson forest // Transactions of Karelian Research Centre of Russian Academy of Science. No 6. Mathematical Modeling and Information Technologies. 2026. Pp. 82-88
Keywords: Galton –Watson forest; tree size; limit theorems; rate of convergence; number of trees of a given size
The article studies Galton –Watson forests formed by a critical branching process starting with N particles. It is assumed that the total number of descendants of the initial particles is n until the process extinction. The number of offspings of each particle has the distribution
pk = h(k + 1) / (k + 1)τ, k=0, 1, 2, . . . , τ ∈ (2, 3),
where the function h(x) is slowly varying at infinity. Let μr be the number of trees with r vertices. Theorems are proven for the rate of convergence of μr distributions to the normal law if N, n, r→∞ and n/N C < ∞.
pk = h(k + 1) / (k + 1)τ, k=0, 1, 2, . . . , τ ∈ (2, 3),
where the function h(x) is slowly varying at infinity. Let μr be the number of trees with r vertices. Theorems are proven for the rate of convergence of μr distributions to the normal law if N, n, r→∞ and n/N C < ∞.
DOI: 10.17076/mat2302
Indexed at RSCI, RSCI (WS)
Last modified: July 3, 2026