FUNCTIONAL CENTRAL LIMIT THEOREM FOR HEAVY TAILED STATIONARY INFINITELY DIVISIBLE PROCESSES GENERATED BY CONSERVATIVE FLOWS

• 成果类型: Article
• 署名作者: Owada, Takashi; Samorodnitsky, Gennady
• 署名单位: Cornell University; Cornell University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/13-AOP899
• 发表日期: 2015
• 页码: 240-285
• 关键词: ergodic properties; Moving averages; local-times; transformations; approximation; CONVERGENCE; sums

摘要

We establish a new class of functional central limit theorems for partial sum of certain symmetric stationary infinitely divisible processes with regularly varying Levy measures. The limit process is a new class of symmetric stable self-similar processes with stationary increments that coincides on a part of its parameter space with a previously described process. The normalizing sequence and the limiting process are determined by the ergodic-theoretical properties of the flow underlying the integral representation of the process. These properties can be interpreted as determining how long the memory of the stationary infinitely divisible process is. We also establish functional convergence, in a strong distributional sense, for conservative pointwise dual ergodic maps preserving an infinite measure.