Set-Valued Stochastic Integrals

Michał Kisielewicz
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Michał Kisielewicz: University of Zielona Góra

Chapter Chapter 3 in Stochastic Differential Inclusions and Applications, 2013, pp 103-145 from Springer

Abstract: Abstract This chapter is devoted to basic notions of the theory of set-valued stochastic integrals. In Sect. 1, we present properties of functional set-valued stochastic integrals defined, like Aumann integrals, as images of subtrajectory integrals of set-valued stochastic processes by some linear mappings with values in $${\mathbb{L}}^{2}(\Omega, \mathcal{F}_{T}, {\mathbb{R}}^{d})$$ . The set-valued stochastic integrals defined in Sect. 2 are understood as certain set-valued random variables.

Keywords: Conditional Expectation; Random Parameter; Stochastic Integral; Compact Convex Subset; Nonempty Closed Subset (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4614-6756-4_3

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DOI: 10.1007/978-1-4614-6756-4_3

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