On a Set-Valued Young Integral with Applications to Differential Inclusions

Laure Coutin (1) , Nicolas Marie (2) , Paul Raynaud de Fitte (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 MODAL'X - Modélisation aléatoire de Paris X
3 LMRS - Laboratoire de Mathématiques Raphaël Salem

We present a new Aumann-like integral for a Hölder multifunction with respect to a Hölder signal, based on the Young integral of a particular set of Hölder selections. This restricted Aumann integral has continuity properties that allow for numerical approximation as well as an existence theorem for an abstract stochastic differential inclusion. This is applied to concrete examples of first order and second order stochastic differential inclusions directed by fractional Brownian motion.

Mots clés: Set-valued integral; Aumann integral; Young integral

Domaines: Probabilités [math.PR]

Laure Coutin, Nicolas Marie, Paul Raynaud de Fitte. On a Set-Valued Young Integral with Applications to Differential Inclusions. Journal of Mathematical Analysis and Applications, 2022, 512 (1), 22 p. ⟨10.1016/j.jmaa.2022.126104⟩. ⟨hal-03252856v2⟩