Scaling limit of the local time of random walks conditioned to stay positive

被引：0
|
作者：
Hong, Wenming [1 ,2 ]
Sun, Mingyang [1 ,2 ]
机构：
[1] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China
[2] Beijing Normal Univ, Lab Math & Complex Syst, Beijing 100875, Peoples R China
来源：
JOURNAL OF APPLIED PROBABILITY | 2024年 / 61卷 / 03期
关键词：
Random walk; Bessel process; local time; conditioning to stay positive; CONVERGENCE; MEANDER; THEOREM;
D O I：
10.1017/jpr.2023.102
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We prove that the local time of random walks conditioned to stay positive converges to the corresponding local time of three-dimensional Bessel processes by proper scaling. Our proof is based on Tanaka's pathwise construction for conditioned random walks and the derivation of asymptotics for mixed moments of the local time.
引用
收藏
页码：1060 / 1074
页数：15
相关论文
共 50 条
  • [21] Conditioned local limit theorems for random walks defined on finite Markov chains
    Ion Grama
    Ronan Lauvergnat
    Émile Le Page
    [J]. Probability Theory and Related Fields, 2020, 176 : 669 - 735
  • [22] Space-time continuous limit of random walks with hyperbolic scaling
    Soga, Kohei
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2014, 102 : 264 - 271
  • [23] Random walk conditioned to stay positive
    Biggins, JD
    [J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2003, 67 : 259 - 272
  • [24] On the probability that integrated random walks stay positive
    Vysotsky, Vladislav
    [J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2010, 120 (07) : 1178 - 1193
  • [25] On Some Lattice Random Walks Conditioned to Stay in Weyl Chambers
    Despax, V
    [J]. MARKOV PROCESSES AND RELATED FIELDS, 2018, 24 (05) : 733 - 758
  • [26] Scaling limit of the collision measures of multiple random walks
    Dinh-Toan Nguyen
    [J]. ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2023, 20 (02): : 1385 - 1410
  • [27] Scaling limit of local time of Sinai’s random walk
    Wenming Hong
    Hui Yang
    Ke Zhou
    [J]. Frontiers of Mathematics in China, 2015, 10 : 1313 - 1324
  • [28] Scaling limit of local time of Sinai's random walk
    Hong, Wenming
    Yang, Hui
    Zhou, Ke
    [J]. FRONTIERS OF MATHEMATICS IN CHINA, 2015, 10 (06) : 1313 - 1324
  • [29] RANDOM WALKS CONDITIONED TO STAY IN WEYL CHAMBERS OF TYPE C AND D
    Koenig, Wolfgang
    Schmid, Patrick
    [J]. ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2010, 15 : 286 - 296
  • [30] Random walks conditioned to stay nonnegative and branching processes in an unfavourable environment
    Vatutin, Vladimir A.
    Dong, Congzao
    Dyakonova, Elena E.
    [J]. SBORNIK MATHEMATICS, 2023, 214 (11) : 1501 - 1533
12345