Resumen de Young and rough differential inclusions

Ismaël Bailleul, Antoine Brault, Laure Coutin

• 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