Self-Standardized Central Limit Theorems for Trimmed Lévy Processes

David M. Mason ()
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David M. Mason: University of Delaware

Journal of Theoretical Probability, 2021, vol. 34, issue 4, 2117-2144

Abstract: Abstract We prove under general conditions that a trimmed subordinator satisfies a self-standardized central limit theorem (SSCLT). Our basic tool is a powerful distributional approximation result of Zaitsev (Probab Theory Relat Fields 74:535–566, 1987). Among other results, we obtain as special cases of our subordinator result the recent SSCLTs of Ipsen et al. (Stoch Process Appl 130:2228–2249, 2020) for trimmed subordinators and a trimmed subordinator analog of a central limit theorem of Csörgő et al. (Probab Theory Relat Fields 72:1–16, 1986) for intermediate trimmed sums in the domain of attraction of a stable law. We then use our methods to prove a similar theorem for general Lévy processes.

Keywords: Trimmed Lévy processes; Trimmed subordinators; Distributional approximation; 60F05; 60G51 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-020-01021-0

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