A characterization of m-dependent stationary infinitely divisible sequences with applications to weak convergence

• 成果类型: Article
• 署名作者: Harrelson, D; Houdré, C
• 署名单位: Hope College; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University System of Georgia; Georgia Institute of Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2003
• 页码: 849-881
• 关键词: stable limit-theorems; random-variables; Moving averages; random vectors; sums

摘要

m-dependent stationary infinitely divisible sequences are characterized as a class of generalized finite moving average sequences via the structure of the associated Levy measure. This characterization is used to find necessary and sufficient conditions for the weak convergence of centered and normalized partial sums of m-dependent stationary infinitely divisible sequences. Partial sum convergence for stationary infinitely divisible sequences that can be approximated by m-dependent ones is then studied.