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Pré-Publication, Document De Travail Année : 2019

Young and rough differential inclusions

Antoine Brault
Laure Coutin
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Résumé

We define in this work a notion of Young differential inclusion dz t P F pz t qdx t , for an α-Hölder control x, with α ą 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 r0, 1s has a selection with finite p-variation, for p ą 1{γ. We also give a notion of solution to the rough differential inclusion dz t P F pz t qdt`Gpz t qdX t , for an α-Hölder rough path X with α P`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

  • HAL Id : hal-02148440 , version 1

Citer

Ismaël Bailleul, Antoine Brault, Laure Coutin. Young and rough differential inclusions. 2019. ⟨hal-02148440v1⟩

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