Affiliation:
1. Wroclaw University Institute of Mathematics Plac Grunwaldzki 2/4 50-384 Wroclaw Poland
Abstract
Abstract
Let K be a fixed proper convex cone contained in a separable Banach space E. Our main result in this note is a construction of a fuzzy process taking values in K-positive fuzzy sets, i.e. in a cone
F
c
c
o
n
v
K
(
E
)
$ \mathcal F_{\mathrm{cconv}}^{K}(E) $
of fuzzy sets contained in K. We prove that this process can be considered as a fuzzy Lévy subordinator (with values in
F
c
c
o
n
v
K
(
E
)
$ \mathcal F_{\mathrm{cconv}}^{K}(E) $
) or simply fuzzy
F
c
c
o
n
v
K
(
E
)
$ \mathcal F_{\mathrm{cconv}}^{K}(E) $
-subordinator.
Reference20 articles.
1. APPLEBAUM, D.: Lévy processes–from probability theory to finance and quantum groups Notices Amer. Math. Soc. 51 (2004), 1336–1347.
2. BARNDORFF-NIELSEN, O. E.—MIKOSCH, T.—RESNICK, S. (eds.): Lévy Processes: Theory and Applications, Birkhäuser, 2001.
3. DIAMOND, P.—KLOEDEN, P.: Metric spaces of fuzzy sets Fuzzy Sets and Systems 35 (1990), 241–249.
4. DIAMOND, P.—KLOEDEN P.: Metric spaces of fuzzy sets Fuzzy Sets and Systems 100 (Suplement) (1999), 63–71.
5. FREMLIN, D. H.: Measure Theory vol. 3., Torres Fremlin, Essex.