Electronic Journal of Probability

Semi-martingales and rough paths theory

Laure Coutin and Antoine Lejay

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Abstract

We prove that the theory of rough paths, which is used to define path-wise integrals and path-wise differential equations, can be used with continuous semi-martingales. We provide then an almost sure theorem of type Wong-Zakai. Moreover, we show that the conditions UT and UCV, used to prove that one can interchange limits and Ito or Stratonovich integrals, provide the same result when one uses the rough paths theory.

Article information

Source
Electron. J. Probab., Volume 10 (2005), paper no. 23, 761-785.

Dates
Accepted: 14 July 2005
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464816824

Digital Object Identifier
doi:10.1214/EJP.v10-162

Mathematical Reviews number (MathSciNet)
MR2164030

Zentralblatt MATH identifier
1109.60035

Subjects
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60H05: Stochastic integrals

Keywords
Semi-martingales $p$-variation iterated integrals rough paths Wong-Zakai theorem conditions UT and UCV

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Coutin, Laure; Lejay, Antoine. Semi-martingales and rough paths theory. Electron. J. Probab. 10 (2005), paper no. 23, 761--785. doi:10.1214/EJP.v10-162. https://projecteuclid.org/euclid.ejp/1464816824


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