2024/01/27 by Lu, Penghui, Li, Yuqiang, Yao, Qiang
#FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2401.15445
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 σ--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.