On \((p,q)\)-rough paths

DOI10.1016/j.jde.2006.01.018zbMath1097.60048OpenAlexW2073113747MaRDI QIDQ2496725

Nicolas Victoir, Antoine Lejay

Publication date: 20 July 2006

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2006.01.018

zbMATH Keywords

controlled differential equationHölder continuous pathsItô and Stratonovich integrals for semi-martingales

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Ordinary differential equations and systems with randomness (34F05)

Related Items (20)

Good rough path sequences and applications to anticipating stochastic calculus ⋮ Global Solutions to Rough Differential Equations with Unbounded Vector Fields ⋮ Perturbed linear rough differential equations ⋮ Sensitivity of rough differential equations: an approach through the omega lemma ⋮ The non-linear sewing lemma III: stability and generic properties ⋮ Time reversal of Volterra processes driven stochastic differential equations ⋮ Differential Equations Driven byΠ-Rough Paths ⋮ Some remarks on the numerical approximation of stochastic differential equations ⋮ Paracontrolled distribution approach to stochastic Volterra equations ⋮ Euler estimates for rough differential equations ⋮ Geometric versus non-geometric rough paths ⋮ Stochastic differential equations driven by processes generated by divergence form operators I: a Wong-Zakai theorem ⋮ Stochastic differential equations driven by processes generated by divergence form operators II: convergence results ⋮ Pathwise Itô calculus for rough paths and rough PDEs with path dependent coefficients ⋮ The non-linear sewing lemma. II. Lipschitz continuous formulation ⋮ Rough path limits of the Wong-Zakai type with a modified drift term ⋮ An isomorphism between branched and geometric rough paths ⋮ Yet another introduction to rough paths ⋮ Constructing general rough differential equations through flow approximations ⋮ Rough path recursions and diffusion approximations

Cites Work

• Semi-martingales and rough paths theory
• Differential equations driven by rough signals
• Extending the Wong-Zakai theorem to reversible Markov processes
• On the convergence of stochastic integrals driven by processes converging on account of a homogenization property
• A note on the notion of geometric rough paths
• An inequality of the Hölder type, connected with Stieltjes integration
• Integration of Paths--A Faithful Representation of Paths by Noncommutative Formal Power Series
• System Control and Rough Paths
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