ROUGH SEMIMARTINGALES AND p-VARIATION ESTIMATES FOR MARTINGALE TRANSFORMS

• 成果类型: Article
• 署名作者: Friz, Peter K.; Zorin-Kranich, Pavel
• 署名单位: Technical University of Berlin; University of Bonn
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/22-AOP1598
• 发表日期: 2023
• 页码: 397-441
• 关键词: differential-equations driven; jump inequalities; brownian-motion; paths; integration

摘要

We establish a new scale of p-variation estimates for martingale para-products, martingale transforms and Ito integrals, of relevance in rough paths theory, stochastic and harmonic analysis. As an application, we introduce rough semimartingales, a common generalization of classical semimartin-gales and (controlled) rough paths and their integration theory.