Aumann Stochastic Integrals

Michał Kisielewicz
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Michał Kisielewicz: University of Zielona Góra

Chapter Chapter 4 in Set-Valued Stochastic Integrals and Applications, 2020, pp 107-139 from Springer

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

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-40329-4_4

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DOI: 10.1007/978-3-030-40329-4_4

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