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Article Dans Une Revue Revista Matemática Iberoamericana Année : 2021

Young and rough differential inclusions

Résumé

We define in this work a notion of Young differential inclusion dz_t ∈ F(z_t) dx_t , 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 dz_t ∈ F(z_t) dt+G(z_t) dX_t , for an α-Hölder rough path X with α ∈ (1/3 , 1/2] , a set-valued map F and a single-valued one form G. Then, we prove the existence of a solution to the inclusion when F is bounded and lower semi-continuous with compact values, or upper semi-continuous with compact and convex values.
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Dates et versions

hal-02148440 , version 1 (05-06-2019)
hal-02148440 , version 2 (07-09-2020)

Identifiants

Citer

Ismaël Bailleul, Antoine Brault, Laure Coutin. Young and rough differential inclusions. Revista Matemática Iberoamericana, 2021, 37 (4), pp.1489 - 1512. ⟨10.4171/rmi/1236⟩. ⟨hal-02148440v2⟩
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