Rules of calculus in the path integral representation of white noise Langevin equations

Abstract : The definition and manipulation of Langevin equations with multiplicative white noise require special care (one has to specify the time discretisation and a stochastic chain rule has to be used to perform changes of variables). While discretisation-scheme transformations and non-linear changes of variable can be safely performed on the Langevin equation, these same transformations lead to inconsistencies in its path-integral representation. We identify their origin and we show how to extend the well-known Itō prescription (dB²=dt) in a way that defines a modified stochastic calculus to be used inside the path-integral representation of the process, in its Onsager-Machlup form.
Type de document :
Pré-publication, Document de travail
35 pages, 2 figures. 2017
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01508497
Contributeur : Vivien Lecomte <>
Soumis le : vendredi 14 avril 2017 - 11:46:17
Dernière modification le : lundi 29 mai 2017 - 14:32:30

Identifiants

  • HAL Id : hal-01508497, version 1
  • ARXIV : 1704.03501

Collections

UPMC | LIPHY | LPTHE | UGA | USPC | PMA

Citation

Leticia F. Cugliandolo, Vivien Lecomte. Rules of calculus in the path integral representation of white noise Langevin equations. 35 pages, 2 figures. 2017. 〈hal-01508497〉

Partager

Métriques

Consultations de la notice

280