Abstract
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.
Funding Statement
PKF has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 683164) and the DFG Research Unit FOR 2402. PZ was partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC-2047/1–390685813.
Acknowledgments
We thank the anonymous referees for their detailed reports that helped to improve this article.
PFK is also affiliated with and WIAS.
Citation
Peter K. Friz. Pavel Zorin-Kranich. "Rough semimartingales and p-variation estimates for martingale transforms." Ann. Probab. 51 (2) 397 - 441, March 2023. https://doi.org/10.1214/22-AOP1598
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