Young and rough differential inclusions

  • Ismaël Bailleul

    Université de Rennes 1, France
  • Antoine Brault

    Université de Paris, France, and Universidad de Chile, Santiago, Chile
  • Laure Coutin

    Université Paul Sabatier, Toulouse, France
Young and rough differential inclusions cover
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We define in this work a notion of Young differential inclusion

for an -Hölder control , with , and give an existence result for such a differential system. As a by-product of our proof, we show that a bounded, compact-valued, -Hölder continuous set-valued map on the interval has a selection with finite -variation, for . We also give a notion of solution to the rough differential inclusion

for an -Hölder rough path with , a set-valued map and a single-valued one form . Then, we prove the existence of a solution to the inclusion when is bounded and lower semi-continuous with compact values, or upper semi-continuous with compact and convex values.

Cite this article

Ismaël Bailleul, Antoine Brault, Laure Coutin, Young and rough differential inclusions. Rev. Mat. Iberoam. 37 (2021), no. 4, pp. 1489–1512

DOI 10.4171/RMI/1236