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 Electronic Journal of Probability > Vol. 10 (2005) > Paper 23 open journal systems 


Semi-martingales and rough paths theory

Laure Coutin, Laboratoire de Statistique et Probabilités, Université Paul Sabatier
Antoine Lejay, Projet OMEGA (INRIA Lorraine/IECN)


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.


Full text: PDF

Pages: 761-785

Published on: July 14, 2005
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Electronic Journal of Probability. ISSN: 1083-6489