Levy processes in cones of fuzzy vectors

TL;DR

This paper introduces a novel approach to constructing fuzzy stochastic processes confined within convex cones, extending classical subordinators to the fuzzy vector setting using Banach space techniques.

Contribution

It establishes a new framework relating convex cones in Euclidean space to cones of fuzzy vectors, enabling the construction of fuzzy subordinators within these cones.

Findings

Developed a method to relate convex cones to fuzzy vector cones.

Constructed pairs of fuzzy subordinators and cones of fuzzy vectors.

Extended the theory of subordinators to the fuzzy vector context.

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 \emph{subordinators}) is of course known to be of great importance in the theory and a myriad of applications.\par But fuzzy stochastic processes are considered in this context for the first time in this paper:\par By first relating with each proper convex cone $C$ in $\R^{n}$ a certain cone of fuzzy vectors $C^*$ and subsequently using some specific Banach space techniques we have been able to produce as many pairs $(L^*_t, C^*)$ of fuzzy \L processes $L^*_t$ and cones $C^*$ of fuzzy vectors such that $L^*_t$ are $C^*$-$\,$subordinators.