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| HAL : inria-00092425, version 1 |
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| Potential Analysis 25, 4 (2006) 307-326 |
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| Young integrals and SPDEs |
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| Massimiliano Gubinelli 1Antoine Lejay 2, 3 |
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| (2006) |
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| In this note, we study the non-linear evolution problem dY_t = -A Y_t dt + B(Y_t) dX_t, where X is a \gamma-Hölder continuous function of the time parameter, with values in a distribution space, and -A the generator of an analytical semigroup. Then, we will give some sharp conditions on X in order to solve the above equation in a function space, first in the linear case (for any value of $\gamma$ in (0,1)), and then when B satisfies some Lipschitz type conditions (for \gamma>1/2). The solution of the evolution problem will be understood in the mild sense, and the integrals involved in that definition will be of Young type. |
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| 1 : | Dipartimento di Matematica Applicata (DMA) |
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Università di Pisa |
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| 2 : | 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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| 3 : | OMEGA (INRIA Sophia Antipolis / INRIA Lorraine / IECN) |
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CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II |
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| Domaine | : | Mathématiques/Analyse fonctionnelle Mathématiques/Probabilités |
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| stochastic heat equation – fractional Brownian motion – pathwise stochastic integration – rough path theory |
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| Liste des fichiers attachés à ce document : | |||||
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| inria-00092425, version 1 | |
| http://hal.inria.fr/inria-00092425 | |
| oai:hal.inria.fr:inria-00092425 | |
| Contributeur : Antoine Lejay | |
| Soumis le : Dimanche 10 Septembre 2006, 12:56:36 | |
| Dernière modification le : Lundi 4 Juin 2007, 17:27:11 | |
