Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion

• 成果类型: Article
• 署名作者: Burdzy, Krzysztof; Nualart, David; Swanson, Jason
• 署名单位: University of Washington; University of Washington Seattle; University of Kansas; State University System of Florida; University of Central Florida
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-013-0511-2
• 发表日期: 2014
• 页码: 237-272
• 关键词: multiple stochastic integrals; central limit-theorems; functionals

摘要

The purpose of this paper is to study the convergence in distribution of two subsequences of the signed cubic variation of the fractional Brownian motion with Hurst parameter . We prove that, under some conditions on both subsequences, the limit is a two-dimensional Brownian motion whose components may be correlated and we find explicit formulae for its covariance function.