无限颜色的A.s.收敛Pólya与随机漫步相关的回合

IF 0.8 4区数学 Q2 MATHEMATICS

Arkiv for Matematik Pub Date : 2018-03-12 DOI:10.4310/arkiv.2021.v59.n1.a4

S. Janson

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引用次数: 6

摘要

我们在两个相关的版本中考虑具有无限多种颜色的随机漫步类型的P\'olya回合。我们表明，在重新缩放后，颜色分布收敛到正态分布，只假设偏移分布上的第二矩。这改进了Bandyopadhyay和Thacker (2014- 2017;收敛概率)，Mailler和markkert (2017;A.s.收敛假设指数矩)。

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A.s. convergence for infinite colour Pólya urns associated with random walks

We consider P\'olya urns with infinitely many colours that are of a random walk type, in two related version. We show that the colour distribution a.s., after rescaling, converges to a normal distribution, assuming only second moments on the offset distribution. This improves results by Bandyopadhyay and Thacker (2014--2017; convergence in probability), and Mailler and Marckert (2017; a.s. convergence assuming exponential moment).

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来源期刊

Arkiv for Matematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishing research papers, of short to moderate length, in all fields of mathematics.