Rough semimartingales and $p$-variation estimates for martingale transforms
Probability
2023-03-22 v2 Classical Analysis and ODEs
Abstract
We establish a new scale of -variation estimates for martingale paraproducts, martingale transforms, and It\^o 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.
Keywords
Cite
@article{arxiv.2008.08897,
title = {Rough semimartingales and $p$-variation estimates for martingale transforms},
author = {Peter Friz and Pavel Zorin-Kranich},
journal= {arXiv preprint arXiv:2008.08897},
year = {2023}
}
Comments
v2: 40 pages, corrected following referee reports