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Set-Valued Functions of Bounded Generalized Variation and Set-Valued Young Integrals

Author

Listed:
  • Mariusz Michta

    (University of Zielona Góra)

  • Jerzy Motyl

    (University of Zielona Góra)

Abstract

The paper deals with some properties of set-valued functions having bounded Riesz p-variation. Set-valued integrals of Young type for such multifunctions are introduced. Selection results and properties of such set-valued integrals are discussed. These integrals contain as a particular case set-valued stochastic integrals with respect to a fractional Brownian motion, and therefore, their properties are crucial for the investigation of solutions to stochastic differential inclusions driven by a fractional Brownian motion.

Suggested Citation

  • Mariusz Michta & Jerzy Motyl, 2022. "Set-Valued Functions of Bounded Generalized Variation and Set-Valued Young Integrals," Journal of Theoretical Probability, Springer, vol. 35(1), pages 528-549, March.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:1:d:10.1007_s10959-020-01059-0
    DOI: 10.1007/s10959-020-01059-0
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    References listed on IDEAS

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    1. Michał Kisielewicz, 2013. "Stochastic Differential Inclusions," Springer Optimization and Its Applications, in: Stochastic Differential Inclusions and Applications, edition 127, chapter 0, pages 147-179, Springer.
    2. Hiai, Fumio & Umegaki, Hisaharu, 1977. "Integrals, conditional expectations, and martingales of multivalued functions," Journal of Multivariate Analysis, Elsevier, vol. 7(1), pages 149-182, March.
    3. Michał Kisielewicz, 2013. "Stochastic Differential Inclusions and Applications," Springer Optimization and Its Applications, Springer, edition 127, number 978-1-4614-6756-4, June.
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