INVARIANCE PRINCIPLES FOR INTEGRATED RANDOM WALKS CONDITIONED TO STAY POSITIVE

被引：0

作者：

Baer, Michael ^{[1
]}

Duraj, Jetlir ^{[2
]}

Wachtel, Vitali ^{[3
]}

机构：

[1] MSG Syst AG, Ismaning, Germany

[2] Univ Pittsburgh, Dept Econ, Pittsburgh, PA USA

[3] Bielefeld Univ, Fac Math, Bielefeld, Germany

来源：

ANNALS OF APPLIED PROBABILITY | 2023年 / 33卷 / 01期

关键词：

Random walk harmonic function; invariance principle; h-transform; Kolmogorov diffusion; PERSISTENCE PROBABILITIES;

D O I：

10.1214/22-AAP1811

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：

Let S (n) be a centered random walk with finite second moment. We con-sider the integrated random walk T (n) = S(0) + S(1) + center dot center dot center dot + S(n). We prove invariance principles for the meander and for the bridge of this process, un-der the condition that the integrated random walk remains positive. Further-more, we prove the functional convergence of its Doob's h-transform to the h-transform of the Kolmogorov diffusion conditioned to stay positive.

引用

页码：127 / 160

页数：34

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