Aumann Stochastic Integrals

  • Michał Kisielewicz
Part of the Springer Optimization and Its Applications book series (SOIA, volume 157)


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.


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Authors and Affiliations

  • Michał Kisielewicz
    • 1
  1. 1.Faculty of MathematicsUniversity of Zielona GóraZielona GóraPoland

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