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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-03252856
Contributor : Nicolas Marie Connect in order to contact the contributor
Submitted on : Saturday, February 19, 2022 - 11:59:35 AM
Last modification on : Wednesday, June 1, 2022 - 3:59:55 AM

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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, Elsevier, 2022, 512 (1), 22 p. ⟨10.1016/j.jmaa.2022.126104⟩. ⟨hal-03252856v2⟩

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