A TREE APPROACH TO p-VARIATION AND TO INTEGRATION

• 成果类型: Article
• 署名作者: Picard, Jean
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Clermont Auvergne (UCA)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/07-AOP388
• 发表日期: 2008
• 页码: 2235-2279
• 关键词: differential-equations driven; fractional brownian motions; branching-processes; Levy processes; excursions; index; paths

摘要

We consider a real-valued path; it is possible to associate a tree to this path. and we explore the relations between the tree. the properties of p-variation of the path. and integration with respect to the path. In particular. the fractal dimension of the tree is estimated from the variations of the path, and Young integrals with respect to the path, as well as integrals from the rough paths theory, are written as integrals on the tree. Examples include sortie stochastic paths such as martingales, Levy processes and fractional Brownian motions (for which an estimator of the Hurst parameter is given).