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

Mariusz Michta () and Jerzy Motyl ()
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Mariusz Michta: University of Zielona Góra
Jerzy Motyl: University of Zielona Góra

Journal of Theoretical Probability, 2022, vol. 35, issue 1, 528-549

Abstract: 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.

Keywords: Hölder continuity; Set-valued function; Set-valued Riesz p-variation; Set-valued Young integral; Selection; Generalized Steiner center; Primary 26A33; Secondary 26A16; 26A45; 28B20; 47H04 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-020-01059-0

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