A CLT FOR EMPIRICAL PROCESSES INVOLVING TIME-DEPENDENT DATA

• 成果类型: Article
• 署名作者: Kuelbs, James; Kurtz, Thomas; Zinn, Joel
• 署名单位: University of Wisconsin System; University of Wisconsin Madison; Texas A&M University System; Texas A&M University College Station
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP711
• 发表日期: 2013
• 页码: 785-816
• 关键词: limit-theorems; CONVERGENCE

摘要

For stochastic processes {X-t : t is an element of E}, we establish sufficient conditions for the empirical process based on {I-Xt <= y - Pr(X-t <= y) : t is an element of E, y is an element of R} to satisfy the CLT uniformly in t is an element of E, y is an element of R. Corollaries of our main result include examples of classical processes where the CLT holds, and we also show that it fails for Brownian motion tied down at zero and E = [0, 1].