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End date: 2024 × Start date: 2020 × End date: 2019 × Start date: 2011 × Type: Report × Subject: Rough paths × WGL Institute: WIAS ×

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    The geometry of the space of branched rough paths
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Tapia, Nikolas; Zambotti, Lorenzo
    We construct an explicit transitive free action of a Banach space of Hölder functions on the space of branched rough paths, which yields in particular a bijection between theses two spaces. This endows the space of branched rough paths with the structure of a principal homogeneous space over a Banach space and allows to characterize its automorphisms. The construction is based on the Baker-Campbell-Hausdorff formula, on a constructive version of the Lyons-Victoir extension theorem and on the Hairer-Kelly map, which allows to describe branched rough paths in terms of anisotropic geometric rough paths.
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    Rough nonlocal diffusions
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Coghi, Michele; Nilssen, Torstein
    We consider a nonlinear Fokker-Planck equation driven by a deterministic rough path which describes the conditional probability of a McKean-Vlasov diffusion with "common" noise. To study the equation we build a self-contained framework of non-linear rough integration theory which we use to study McKean-Vlasov equations perturbed by rough paths. We construct an appropriate notion of solution of the corresponding Fokker-Planck equation and prove well-posedness.