Young and rough differential inclusions

• Ismaël Bailleul ^[2] ; Antoine Brault ^[3] ; Laure Coutin ^[1]
  1. [1] Paul Sabatier University

     Paul Sabatier University

     Arrondissement de Toulouse, Francia

     
  2. [2] Université de Rennes 1
  3. [3] Université de Paris

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 37, Nº 4, 2021, págs. 1489-1512
• Idioma: inglés
• DOI: 10.4171/rmi/1236
• Texto completo no disponible (Saber más ...)
• Resumen

  • We define in this work a notion of Young differential inclusion dzt∈F(zt)dxt, for an α-Hölder control x, with α>1/2, and give an existence result for such a differential system. As a by-product of our proof, we show that a bounded, compact-valued, γ-Hölder continuous set-valued map on the interval [0,1] has a selection with finite p-variation, for p>1/γ. We also give a notion of solution to the rough differential inclusion dzt∈F(zt)dt+G(zt)dXt