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Set-Valued Stochastic Integrals

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Stochastic Differential Inclusions and Applications

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 80))

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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.

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  1. Faculty of Mathematics, University of Zielona Góra, Zielona Góra, Poland

    Michał Kisielewicz

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Kisielewicz, M. (2013). Set-Valued Stochastic Integrals. In: Stochastic Differential Inclusions and Applications. Springer Optimization and Its Applications, vol 80. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6756-4_3

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