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

We present a new Aumann-like integral for a Holder multifunction with respect to a Holder signal, based on the Young integral of a particular set of Holder 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.