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2005 Semi-martingales and rough paths theory
Laure Coutin, Antoine Lejay
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Electron. J. Probab. 10: 761-785 (2005). DOI: 10.1214/EJP.v10-162

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.

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Laure Coutin. Antoine Lejay. "Semi-martingales and rough paths theory." Electron. J. Probab. 10 761 - 785, 2005. https://doi.org/10.1214/EJP.v10-162

Information

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

zbMATH: 1109.60035
MathSciNet: MR2164030
Digital Object Identifier: 10.1214/EJP.v10-162

Subjects:
Primary: 60F17
Secondary: 60H05

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Vol.10 • 2005
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