Quasi-geometric rough paths and rough change of variable formula - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques Année : 2022

Quasi-geometric rough paths and rough change of variable formula

Résumé

Using some basic notions from the theory of Hopf algebras and quasi-shuffle algebras, we introduce rigorously a new family of rough paths: the quasi-geometric rough paths. We discuss their main properties. In particular, we will relate them with iterated Brownian integrals and the concept of "simple bracket extension", developed in the PhD thesis of David Kelly. As a consequence of these results, we have a sufficient criterion to show for any $\gamma\in (0,1)$ and any sufficiently smooth function $\varphi \colon \mathbb{R}^d\to \mathbb{R}$ a rough change of variable formula on any $\gamma$-H\"older continuous path $x\colon [0, T]\to \mathbb{R}^d$, i.e. an explicit expression of $\varphi(x_t)$ in terms of rough integrals.

Dates et versions

hal-03902146 , version 1 (15-12-2022)

Identifiants

Citer

Carlo Bellingeri. Quasi-geometric rough paths and rough change of variable formula. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2022, à paraitre. ⟨hal-03902146⟩
12 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More