独立指标和的迭代和单对数规律，及其在Ginibre点过程和Karlin占用方案中的应用

IF 1.1 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications Pub Date : 2025-02-10 DOI:10.1016/j.spa.2025.104597

Dariusz Buraczewski , Alexander Iksanov , Valeriya Kotelnikova

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引用次数: 0

摘要

在t→∞时，证明了由t参数化且t单调的独立指标无穷和的一个迭代对数定律。结果表明，如果和的期望b和方差a具有可比性，则LIL中的归一化包括a的迭代对数。如果期望增长快于方差，而logb/loga的比值保持有界，则LIL中的归一化包括a的单对数（使LIL成为单对数定律）。将所得结果应用于圆盘上无限Ginibre点过程的点数和Karlin占位方案中的占位盒数及相关量。

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Laws of the iterated and single logarithm for sums of independent indicators, with applications to the Ginibre point process and Karlin’s occupancy scheme

We prove a law of the iterated logarithm (LIL) for an infinite sum of independent indicators parameterized by

t

and monotone in

t

t \to \infty

. It is shown that if the expectation

b

and the variance

a

of the sum are comparable, then the normalization in the LIL includes the iterated logarithm of

a

. If the expectation grows faster than the variance, while the ratio

log b / log a

remains bounded, then the normalization in the LIL includes the single logarithm of

a

(so that the LIL becomes a law of the single logarithm). Applications of our result are given to the number of points of the infinite Ginibre point process in a disk and the number of occupied boxes and related quantities in Karlin’s occupancy scheme.

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来源期刊

Stochastic Processes and their Applications 数学-统计学与概率论

CiteScore

2.90

自引率

7.10%

发文量

180

审稿时长

23.6 weeks

期刊介绍： Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests. Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.