A note on the notion of geometric rough paths

DOI10.1007/s00440-005-0487-7zbMath1108.34052arXivmath/0403115OpenAlexW1977726118MaRDI QIDQ2509001

Nicolas Victoir, Peter K. Friz

Publication date: 16 October 2006

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0403115

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Geometric methods in ordinary differential equations (34A26) Sample path properties (60G17) Ordinary differential equations and systems with randomness (34F05)

Related Items (32)

Expected signature of stopped Brownian motion on \(d\)-dimensional \(C^{2, \alpha }\)-domains has finite radius of convergence everywhere: \(2 \leq d \leq 8\) ⋮ Transport and continuity equations with (very) rough noise ⋮ Good rough path sequences and applications to anticipating stochastic calculus ⋮ Solving the KPZ equation ⋮ Rough integration via fractional calculus ⋮ A Fubini type theorem for rough integration ⋮ Smoothness of densities for area-like processes of fractional Brownian motion ⋮ Optimal Execution with Rough Path Signatures ⋮ Time reversal of Volterra processes driven stochastic differential equations ⋮ Malliavin calculus and rough paths ⋮ Differential structure and flow equations on rough path space ⋮ Gaussian convergence for stochastic acceleration of \(\mathcal {N}\) particles in the dense spectrum limit ⋮ A Lévy area between Brownian motion and rough paths with applications to robust nonlinear filtering and rough partial differential equations ⋮ A theory of regularity structures ⋮ A Stratonovich-Skorohod integral formula for Gaussian rough paths ⋮ On uniformly subelliptic operators and stochastic area ⋮ An extension theorem to rough paths ⋮ Euler estimates for rough differential equations ⋮ Geometric versus non-geometric rough paths ⋮ Densities for rough differential equations under Hörmander's condition ⋮ Stochastic differential equations driven by processes generated by divergence form operators I: a Wong-Zakai theorem ⋮ On \((p,q)\)-rough paths ⋮ Differential equations driven by Gaussian signals ⋮ Stochastic differential equations driven by processes generated by divergence form operators II: convergence results ⋮ A generalized Fernique theorem and applications ⋮ Discretely sampled signals and the rough Hoff process ⋮ Non-degeneracy of Wiener functionals arising from rough differential equations ⋮ Rough path limits of the Wong-Zakai type with a modified drift term ⋮ Partial differential equations driven by rough paths ⋮ Yet another introduction to rough paths ⋮ Geometric rough paths on infinite dimensional spaces ⋮ The support of singular stochastic partial differential equations

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