Lévy Subordinators in Cones of Fuzzy Sets

Jan Schneider () and Roman Urban ()
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Jan Schneider: Wroclaw University of Science and Technology
Roman Urban: Wroclaw University

Journal of Theoretical Probability, 2019, vol. 32, issue 4, 1909-1924

Abstract: Abstract The general problem of how to construct stochastic processes which are confined to stay in a predefined cone (in the one-dimensional but also multi-dimensional case also referred to as subordinators) is of course known to be of great importance in the theory and a myriad of applications. In this paper we see how this may be dealt with on the metric space of fuzzy sets/vectors: By first relating with each proper convex cone C in $$\mathbb {R}^{n}$$ R n a certain cone of fuzzy vectors $$C^*$$ C ∗ and subsequently using some very specific Banach space techniques we have been able to produce as many pairs $$(L^*_t, C^*)$$ ( L t ∗ , C ∗ ) of fuzzy Lévy processes $$L^*_t$$ L t ∗ and cones $$C^*$$ C ∗ of fuzzy vectors such that $$L^*_t$$ L t ∗ are $$C^*$$ C ∗ -subordinators.

Keywords: Lévy processes in Banach spaces; K-positive fuzzy Lévy process; Cone-subordinators; Cones in Banach spaces; Pettis integral; Bochner integral; Convex sets; Fuzzy sets; Fuzzy vectors; Support function; Hausdorff distance; G0G51; 60G20; 46C05 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10959-018-0853-x

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