Controlled differential equations as Young integrals: a simple approach - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Journal of Differential Equations Année : 2010

Controlled differential equations as Young integrals: a simple approach

Résumé

The theory of rough paths allows one to define controlled differential equations driven by a path which is irregular. The most simple case is the one where the driving path has finite p-variations with 1≤ p <2, in which case the integrals are interpreted as Young integrals. The prototypal example is given by Stochastic Differential Equations driven by fractional Brownian motion with Hurst index greater than 1/2. Using simple computations, we give the main results regarding this theory --- existence, uniqueness, convergence of the Euler scheme, flow property, ... --- which are spread out among several articles.
Fichier principal
Vignette du fichier
simple-rde.pdf (206.29 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

inria-00402397 , version 1 (07-07-2009)

Identifiants

Citer

Antoine Lejay. Controlled differential equations as Young integrals: a simple approach. Journal of Differential Equations, 2010, 249, pp.1777-1798. ⟨10.1016/j.jde.2010.05.006⟩. ⟨inria-00402397⟩
253 Consultations
899 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More