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| HAL : inria-00402397, version 1 |
| DOI : 10.1016/j.jde.2010.05.006 |
| Voir la fiche détaillée |  BibTeX,EndNote,... |
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| Journal of Differential Equations 249 (2010) 1777-1798 |
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| Controlled differential equations as Young integrals: a simple approach |
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| Antoine Lejay 1, 2 |
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| (2010) |
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| The theory of rough paths allows one to define controlled differential equations driven by a path which is irregular. The most simple case is the one where the driving path has finite p-variations with 1≤ p <2, in which case the integrals are interpreted as Young integrals. The prototypal example is given by Stochastic Differential Equations driven by fractional Brownian motion with Hurst index greater than 1/2. Using simple computations, we give the main results regarding this theory --- existence, uniqueness, convergence of the Euler scheme, flow property, ... --- which are spread out among several articles. |
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| 1 : | Institut Elie Cartan Nancy (IECN) |
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CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine |
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| 2 : | TOSCA (INRIA Sophia Antipolis / INRIA Lorraine / IECN) |
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INRIA – CNRS : UMR7502 – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine |
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| Probabilités et statistique |
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| Domaine | : | Mathématiques/Probabilités Mathématiques/Analyse classique |
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| controlled differential equations – Young integral – fractional Brownian motion – rough paths – flow property – Euler scheme |
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| Liste des fichiers attachés à ce document : | |||||
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| inria-00402397, version 1 | |
| http://hal.inria.fr/inria-00402397 | |
| oai:hal.inria.fr:inria-00402397 | |
| Contributeur : Antoine Lejay | |
| Soumis le : Mardi 7 Juillet 2009, 12:04:58 | |
| Dernière modification le : Mardi 23 Novembre 2010, 15:21:25 | |
