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

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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.

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Authors and Affiliations

  1. Department of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, 00076, Aalto, Finland

    Matti Kiiski

  2. Department of Mathematics, Technische Universität Berlin, Building MA, Str. des 17. Juni 136, 10623, Berlin, Germany

    Ari-Pekka Perkkiö

Authors
  1. Matti Kiiski
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  2. Ari-Pekka Perkkiö
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Correspondence to Ari-Pekka Perkkiö.

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The second author is grateful to the Einstein Foundation for the financial support.

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Kiiski, M., Perkkiö, AP. Optional and Predictable Projections of Normal Integrands and Convex-Valued Processes. Set-Valued Var. Anal 25, 313–332 (2017). https://doi.org/10.1007/s11228-016-0381-8

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  • DOI: https://doi.org/10.1007/s11228-016-0381-8

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