Limit Properties of Record Numbers in Random walks
arxiv(2024)
摘要
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.
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