Aumann Stochastic Integrals

Abstract

In this chapter we present the definition and properties of Aumann stochastic integrals of set-valued stochastic processes \(F:\mathbb {R}^+\times \Omega \rightarrow \mathrm {Cl}(\mathbb {R}^d)\) and subsets of the space \(\mathbb {L}^p(\mathbb {R}^+\times \Omega ,\beta \otimes \mathcal {F},\mathbb {R}^d)\). We begin with the definition and properties of the Aumann integrals of subsets of the space \({\mathbb {L}}^p(T,\mathcal {F},\mu ,X)\), where (X, |⋅|) is a separable Banach space.