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

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arxiv 2008.08897 v2 pith:FMIQNKU2 submitted 2020-08-20 math.PR math.CA

Peter Friz , Pavel Zorin-Kranich This is my paper · ORCID
classification math.PRmath.CA
keywords roughmartingalesemimartingalesestimatespathstheorytransformsvariation
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abstract

We establish a new scale of $p$-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.

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  1. Expected signatures via partial integration, coordinate change and symmetrization

    math.PR 2026-07 conditional novelty 8.0 of 10

    A coordinate transform on the tensor algebra lets expected signatures of augmented rough processes be computed by deterministic integration of Gaussian/polynomial correlators, dramatically reducing numerical cost.

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