An Introduction to Rough Paths

Antoine Lejay 1, 2
1 IECN - Institut Élie Cartan de Nancy
2 OMEGA - Probabilistic numerical methods
CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : This article aims to be an introduction to the theory of rough paths, in which integrals of differential forms against irregular paths and differential equations controlled by irregular paths are defined. This theory makes use of an extension of the notion of iterated integrals of the paths, whose algebraic properties appear to be fundamental. This theory is well-suited for stochastic processes.
Keywords : controlled differential equations integration against irregular paths geometric multiplicative functional Chen series p-variation stochastic processes iterated integrals
Document type :
Book sections
Complete list of metadatas

Cited literature [48 references]  Display  Hide  Download
https://hal.inria.fr/inria-00102184
Contributor : Antoine Lejay <>
Submitted on : Wednesday, February 25, 2009 - 2:12:55 PM
Last modification on : Saturday, January 27, 2018 - 1:31:53 AM
Long-term archiving on: Monday, April 5, 2010 - 11:57:09 PM

File

introduction_to_rough_paths_Se...
Files produced by the author(s)

Identifiers

Collections

INRIA | IECN | CNRS | INSMI | UNIV-LORRAINE

Citation

Antoine Lejay. An Introduction to Rough Paths. J. Azéma; M. Ledoux; M. Emery; M. Yor. Seminaire de Probabilités XXXVII, 1832 (1832), Springer Berlin / Heidelberg, pp.1-59, 2003, Lecture Notes in Mathematics, 978-3-540-20520-3. ⟨10.1007/b94376⟩. ⟨inria-00102184⟩

Export

BibTeX TEI DC DCterms EndNote

Share

Metrics

Record views

491

Files downloads

9560

 

 

Contact

archive-ouverte@inria.fr