David M. Mason (University of Delaware): Self-standardized central limit theorems for trimmed subordinators

We prove under almost no conditions that a trimmed subordinator always satisfies a self-standardized central limit theorem [CLT] at zero. Our basic tools are a classic representation for subordinators and a distributional approximation result of Zaitsev (1987). Among other results, we obtain as a by product a subordinator analog of a CLT of S. Csörgő, Horváth and Mason (1986) for intermediate trimmed sums in the domain of attraction of a stable law. We then show how our methods extend to proving similar theorems for spectrally positive Lévy processes and then to general Lévy processes.