Path-dependent Martingale Problems and Additive Functionals

Abstract : The paper introduces and investigates the natural extension to the path-dependent setup of the usual concept of canonical Markov class introduced by Dynkin and which is at the basis of the theory of Markov processes. That extension, indexed by starting paths rather than starting points will be called path-dependent canonical class. Associated with this is the generalization of the notions of semi-group and of additive functionals to the path-dependent framework. A typical example of such family is constituted by the laws $({\mathbb P}^{s,η})_{(s,\eta) \in {\mathbb R} \times \Omega}$ , where for fixed time s and fixed path η defined on [0, s], $({\mathbb P}^{s,η})_{(s,\eta) \in {\mathbb R} \times \Omega}$ being the (unique) solution of a path-dependent martingale problem or more specifically a weak solution of a path-dependent SDE with jumps, with initial path η. In a companion paper we apply those results to study path-dependent analysis problems associated with BSDEs.
Type de document :
Pré-publication, Document de travail
Liste complète des métadonnées

Littérature citée [19 références]  Voir  Masquer  Télécharger
Contributeur : Francesco Russo <>
Soumis le : mardi 24 avril 2018 - 14:02:37
Dernière modification le : mercredi 23 janvier 2019 - 10:29:31
Document(s) archivé(s) le : mercredi 19 septembre 2018 - 06:37:34


Fichiers produits par l'(les) auteur(s)


  • HAL Id : hal-01775200, version 1
  • ARXIV : 1804.09417


Adrien Barrasso, Francesco Russo. Path-dependent Martingale Problems and Additive Functionals. 2018. 〈hal-01775200〉



Consultations de la notice


Téléchargements de fichiers