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Lévy Subordinators in Cones of Fuzzy Sets

  • Jan Schneider
  • Roman Urban
Article
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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 \(\mathbb {R}^{n}\) a certain cone of fuzzy vectors \(C^*\) and subsequently using some very specific Banach space techniques we have been able to produce as many pairs \((L^*_t, C^*)\) of fuzzy Lévy processes \(L^*_t\) and cones \(C^*\) of fuzzy vectors such that \(L^*_t\) are \(C^*\)-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 

Mathematics Subject Classification (2010)

G0G51 60G20 46C05 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer Science and ManagementWroclaw University of Science and TechnologyWrocławPoland
  2. 2.Institute of MathematicsWroclaw UniversityWrocławPoland

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