Electronic Journal of Probability

Semi-martingales and rough paths theory

Laure Coutin and Antoine Lejay

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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

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

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

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Zentralblatt MATH identifier

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

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

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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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