Limit Properties of Record Numbers in Random walks

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...

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Bibliographic Details
Published in:arXiv.org 2024-01
Main Authors: Lu, Penghui, Li, Yuqiang, Yao, Qiang
Format: Article
Language:English
Subjects:
Deviation
Random walk
Online Access:Get full text
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Summary: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.
ISSN:2331-8422