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Rough semimartingales and $p$-variation estimates for martingale transforms
Peter Friz, Pavel Zorin-Kranich · 2020-08-20 · via math.PR updates on arXiv.org

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.

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