High-frequency Donsker theorems for Levy measures

• 成果类型: Article
• 署名作者: Nickl, Richard; Reiss, Markus; Soehl, Jakob; Trabs, Mathias
• 署名单位: University of Cambridge; Humboldt University of Berlin
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-014-0607-3
• 发表日期: 2016
• 页码: 61-108
• 关键词: CENTRAL LIMIT-THEOREMS; nonparametric-estimation; CONVERGENCE; inference; rates

摘要

Donsker-type functional limit theorems are proved for empirical processes arising from discretely sampled increments of a univariate Levy process. In the asymptotic regime the sampling frequencies increase to infinity and the limiting object is a Gaussian process that can be obtained from the composition of a Brownian motion with a covariance operator determined by the Levy measure. The results are applied to derive the asymptotic distribution of natural estimators for the distribution function of the Levy jump measure. As an application we deduce Kolmogorov-Smirnov type tests and confidence bands.