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Rough semimartingales and \(p\)-variation estimates for martingale transforms. (English) Zbl 1532.60230

Summary: We establish a new scale of \(p\)-variation estimates for martingale paraproducts, martingale transforms and Itô integrals, of relevance in rough paths theory, stochastic and harmonic analysis. As an application, we introduce rough semimartingales, a common generalization of classical semimartingales and (controlled) rough paths and their integration theory.

MSC:

60L20 Rough paths
60G44 Martingales with continuous parameter
60G46 Martingales and classical analysis
60H05 Stochastic integrals

References:

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