We propose a theory of linear differential equations driven by unbounded operator-valued rough signals. As an application we consider rough linear transport equations and more general linear hyperbolic symmetric systems of equations driven by time-dependent vector fields which are only distributions in the time direction.
Nous proposons une théorie des équations différentielles linéaires dirigées par des processus à valeurs opérateurs non bornés. Nous appliquons cette théorie à une équation de transport pris au sens rugueux ainsi qu’à des systèmes d’équations symétriques, linéaires paraboliques dirigées par des champs de vecteurs dépendant du temps. Ces derniers sont des distributions en temps.
Ismael Bailleul 1; Massimiliano Gubinelli 2
@article{AFST_2017_6_26_4_795_0, author = {Ismael Bailleul and Massimiliano Gubinelli}, title = {Unbounded rough drivers}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {795--830}, publisher = {Universit\'e Paul Sabatier, Toulouse}, volume = {Ser. 6, 26}, number = {4}, year = {2017}, doi = {10.5802/afst.1553}, language = {en}, url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1553/} }
TY - JOUR AU - Ismael Bailleul AU - Massimiliano Gubinelli TI - Unbounded rough drivers JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2017 SP - 795 EP - 830 VL - 26 IS - 4 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1553/ DO - 10.5802/afst.1553 LA - en ID - AFST_2017_6_26_4_795_0 ER -
%0 Journal Article %A Ismael Bailleul %A Massimiliano Gubinelli %T Unbounded rough drivers %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2017 %P 795-830 %V 26 %N 4 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1553/ %R 10.5802/afst.1553 %G en %F AFST_2017_6_26_4_795_0
Ismael Bailleul; Massimiliano Gubinelli. Unbounded rough drivers. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 26 (2017) no. 4, pp. 795-830. doi : 10.5802/afst.1553. https://afst.centre-mersenne.org/articles/10.5802/afst.1553/
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