INVARIANCE PRINCIPLES FOR INTEGRATED RANDOM WALKS CONDITIONED TO STAY POSITIVE

• 成果类型: Article
• 署名作者: Baer, Michael; Duraj, Jetlir; Wachtel, Vitali
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh; University of Bielefeld
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1811
• 发表日期: 2023
• 页码: 127-160
• 关键词: persistence probabilities

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.