Asymptotic Probability of Record Numbers in Random Walks  

随机游动记录数的渐进概率

作　　者：PENG Wenjie LI Yuqiang 彭文杰;李育强(华东师范大学统计学院,统计与数据科学前沿理论与应用教育部重点实验室,上海200062)

机构地区：[1]School of statistics,KLATASDS-MOE,East China Normal University,Shanghai,200062,China

出　　处：《应用概率统计》2025年第1期17-27,共11页Chinese Journal of Applied Probability and Statistics

基　　金：supported by the National Natural Science Foundation of China(Grant No.11671145);the Science and Technology Commission of Shanghai Municipality(Grant No.18dz2271000).

摘　　要：In this paper,large deviations principle(LDP)and moderate deviations principle(MDP)of record numbers in random walks are studied under certain conditions.The results show that the rate functions of LDP and MDP are different from those of weak record numbers,which are interesting complements of the conclusions by Li and Yao[1].本文研究了在一定条件下的随机游动中记录数的大偏差和中偏差极限定理.结果表明记录数的大偏差和中偏差的速率函数与弱记录数的相应速率函数有所不同。文章结论是对Li和Yao[1]结果的有趣补充,有助于我们更好地理解随机游动的波动理论.

关 键 词：random walk record number large deviation moderate deviation 

分 类 号：O211.4[理学—概率论与数理统计]