Constructing general rough differential equations through flow approximations - Archive ouverte HAL Access content directly
Journal Articles Electronic Journal of Probability Year : 2022

Constructing general rough differential equations through flow approximations

(1, 2)
1
2

Abstract

The non-linear sewing lemma constructs flows of rough differential equations from a braod class of approximations called almost flows. We consider a class of almost flows that could be approximated by solutions of ordinary differential equations, in the spirit of the backward error analysis. Mixing algebra and analysis, a Taylor formula with remainder and a composition formula are central in the expansion analysis. With a suitable algebraic structure on the non-smooth vector fields to be integrated, we recover in a single framework several results regarding high-order expansions for various kind of driving paths. We also extend the notion of driving rough path. We also introduce as an example a new family of branched rough paths, called aromatic rough paths modeled after aromatic Butcher series.
Fichier principal
Vignette du fichier
Generalized_RDE_VF1.pdf (390.21 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-02871886 , version 1 (17-06-2020)
hal-02871886 , version 2 (04-08-2020)
hal-02871886 , version 3 (16-12-2021)
hal-02871886 , version 4 (13-01-2022)

Identifiers

Cite

Antoine Lejay. Constructing general rough differential equations through flow approximations. Electronic Journal of Probability, 2022, 27, pp.1-24. ⟨10.1214/21-EJP717⟩. ⟨hal-02871886v4⟩
160 View
259 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More