Optional and Predictable Projections of Normal Integrands and Convex-Valued Processes

Matti Kiiski, Ari-Pekka Perkkiö

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1 Citation (Scopus)

Abstract

This article studies optional and predictable projections of integrands and convex-valued stochastic processes. The existence and uniqueness are shown under general conditions that are analogous to those for conditional expectations of integrands and random sets. In the convex case, duality correspondences between the projections and projections of epigraphs are given. These results are used to study projections of set-valued integrands. Consistently with the general theory of stochastic processes, projections are not constructed using reference measures on the optional and predictable sigma-algebras.

Original languageEnglish
Pages (from-to)313-332
Number of pages20
JournalSET-VALUED AND VARIATIONAL ANALYSIS
Volume25
Issue number2
DOIs
Publication statusPublished - Jun 2017
MoE publication typeA1 Journal article-refereed

Keywords

  • Set-valued and variational analysis
  • Normal integrand
  • Set-valued integrand
  • Set-valued stochastic process
  • Optional and predictable projection
  • Convex conjugate

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