Limit Properties of Record Numbers in Random walks

Penghui Lu; Yuqiang Li; Qiang Yao

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arXiv · 2401.15445

Limit Properties of Record Numbers in Random walks

Penghui Lu·Yuqiang Li·Qiang Yao

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Abstract

In this paper, we systematically summarize and enhance the understanding of weak convergence and functional limits of record numbers in discrete-time random walks under Spitzer's condition, and extend these findings to $\sigma$--record numbers using similar methods. Additionally, we identify a sufficient condition for the existence of functional limits for record numbers in continuous-time random walks. Finally, we derive corresponding results for large deviations, moderate deviations, and laws of the iterated logarithm pertaining to record numbers in discrete-time random walks.

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Penghui Lu, Yuqiang Li, Qiang Yao. 2024-01-27. Limit Properties of Record Numbers in Random walks. https://arxiv.org/abs/2401.15445

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