Set-Valued Stochastic Processes

Michał Kisielewicz
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Michał Kisielewicz: University of Zielona Góra

Chapter Chapter 2 in Stochastic Differential Inclusions and Applications, 2013, pp 67-102 from Springer

Abstract: Abstract This chapter is devoted to basic notions of the theory of set-valued mappings and set-valued stochastic processes. We begin with the notions and basic properties of the space of subsets of a given metric space. Selected properties of set-valued mappings, Aumann integrals, and set-valued stochastic processes are presented. The last two parts of this chapter discuss properties of a set-valued conditional expectation and selection properties of set-valued integrals depending on random parameters.

Keywords: Hausdorff Distance; Steiner Point; Continuous Selection; Selection Theorem; Filter Probability Space (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-1-4614-6756-4_2

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