Large Deviations of the Range of the Planar Random Walk on the Scale of the Mean

被引：1

作者：

Liu, Jingjia ^{[1
]}

Vogel, Quirin ^{[2
]}

机构：

[1] Univ Munster, Fachbereich Math & Informat, Einsteinstr 62, D-48149 Munster, Germany

[2] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2021年 / 34卷 / 04期

关键词：

Large deviations; Random walk range; Planar random walk; NUMBER;

D O I：

10.1007/s10959-020-01039-4

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 an upper large deviation bound on the scale of the mean for a symmetric random walk in the plane satisfying certain moment conditions. This result complements the study by Phetpradap for the random walk range, which is restricted to dimension three and higher, and of van den Berg, Bolthausen and den Hollander, for the volume of the Wiener sausage.

引用

页码：2315 / 2345

页数：31

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