Rough semimartingales and $p$-variation estimates for martingale transforms

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.

v2: 40 pages, corrected following referee reports

References in corpus (5)

• Averaging dynamics driven by fractional Brownian motion
• Jump inequalities via real interpolation
• Nonsemimartingales: Stochastic differential equations and weak Dirichlet processes
• Variational estimates for martingale paraproducts
• Weighted Lépingle inequality