A UNIFORM LAW FOR CONVERGENCE TO THE LOCAL TIMES OF LINEAR FRACTIONAL STABLE MOTIONS

• 成果类型: Article
• 署名作者: Duffy, James A.
• 署名单位: University of Oxford; University of Oxford
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1085
• 发表日期: 2016
• 页码: 45-72
• 关键词: nonparametric cointegrating regression; ASYMPTOTIC THEORY; WEAK-CONVERGENCE; sums; functionals; attraction; INTEGRALS; domain; series

摘要

We provide a uniform law for the weak convergence of additive functionals of partial sum processes to the local times of linear fractional stable motions, in a setting sufficiently general for statistical applications. Our results are fundamental to the analysis of the global properties of nonparametric estimators of nonlinear statistical models that involve such processes as covariates.