A note on Lévy subordinators in cones of fuzzy sets in Banach spaces
-
Roman Urban
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
-
(Communicated by Anatolij Dvurečcenskij)
References
[1] APPLEBAUM, D.: Lévy processes–from probability theory to finance and quantum groups Notices Amer. Math. Soc. 51 (2004), 1336–1347.Search in Google Scholar
[2] BARNDORFF-NIELSEN, O. E.—MIKOSCH, T.—RESNICK, S. (eds.): Lévy Processes: Theory and Applications, Birkhäuser, 2001.10.1007/978-1-4612-0197-7Search in Google Scholar
[3] DIAMOND, P.—KLOEDEN, P.: Metric spaces of fuzzy sets Fuzzy Sets and Systems 35 (1990), 241–249.10.1016/0165-0114(90)90197-ESearch in Google Scholar
[4] DIAMOND, P.—KLOEDEN P.: Metric spaces of fuzzy sets Fuzzy Sets and Systems 100 (Suplement) (1999), 63–71.10.1016/S0165-0114(99)80007-4Search in Google Scholar
[5] FREMLIN, D. H.: Measure Theory vol. 3., Torres Fremlin, Essex.Search in Google Scholar
[6] FU, K.-A.—ZHANG, L.-X.: Strong laws of large numbers for arrays of rowwise independent random compact sets and fuzzy random sets Fuzzy Sets and Systems 159 (2008), 3360–3368.10.1016/j.fss.2008.06.012Search in Google Scholar
[7] GIKHMAN, I. I.—SKOROHOD, A. V.: The Theory of Stochastic Processes Vol. II., Springer, Berlin, 1975.Search in Google Scholar
[8] KIGAMI, J.: Analysis on Fractals Cambridge University Press, 2001.10.1017/CBO9780511470943Search in Google Scholar
[9] KYPRIANOU, A. E.: Introductory Lectures on Fluctuations of Lévy Processes with Applications Springer, 2006.Search in Google Scholar
[10] KYPRIANOU, A. E.—SCHOUTENS, W.—WILMOTT, P. (eds.): Exotic Option Pricing and Advanced Lévy Models Wiley, Chichester, 2005.Search in Google Scholar
[11] LI, S.—GUAN, L.: Fuzzy set-valued Gaussian processes and Brownian motions Inform. Sci. 177 (2007), 3251–3259.10.1016/j.ins.2006.11.008Search in Google Scholar
[12] LI, S.—OGURA, Y.—KREINOVICH, V.: Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables. Theory and Decision Library, Series B: Mathematical and Statistical Methods, 43. Kluwer Academic Publishers Group, Dordrecht, 2002.10.1007/978-94-015-9932-0Search in Google Scholar
[13] MUSIA\L, K.: Pettis integral. In: Handbook of Measure Theory, Vol. I, (E. Pap, ed.), Elsevier, Amsterdam, 2002, pp. 531–586.10.1016/B978-044450263-6/50013-0Search in Google Scholar
[14] PéREZ-ABREU, A.—ROCHA-ARTEAGA, A.: On the Lévy-Khintchine representation of Lévy processes in cones of Banach spaces Publ. Mat. Urug. 11 (2006), 41–55.Search in Google Scholar
[15] QUANG, N. V.—THUAN, N. T.: Strong laws of large numbers for adapted arrays of set-valued and fuzzy-valued random variables in Banach space Fuzzy Sets and Systems 209 (2012), 14–32.10.1016/j.fss.2012.04.012Search in Google Scholar
[16] SCHNEIDER, J.—URBAN, R.: Lévy subordinators in cones of fuzzy sets J. Theoret. Probab. 32 (2019), 1909–1924.10.1007/s10959-018-0853-xSearch in Google Scholar
[17] TERáN, P.: An embedding theorem for convex fuzzy sets Fuzzy Sets and Systems 152, (2005), 191–208.10.1016/j.fss.2004.10.003Search in Google Scholar
[18] VIERTL, R.—HARETER, D.: Beschreibung und Analyse unscharfer Information. Statistishe Methoden für unscharfe Daten Springer, Wien, New York, 2005.Search in Google Scholar
[19] VIERTL, R.: Statistical Methods for Fuzzy Data John Wiley & Sons, 2011.10.1002/9780470974414Search in Google Scholar
[20] YOSIDA, K.: Functional Analysis Springer-Verlag, 1971.10.1007/978-3-662-00781-5Search in Google Scholar
© 2022 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Regular Papers
- The poset of morphism-extension classes of countable graphs
- Characterization of monadic BL-algebras by state operators
- Comments on efficient batch verification test for digital signatures based on elliptic curves
- On necessary and sufficient conditions for the monogeneity of a certain class of polynomials
- An exponential Diophantine equation involving the sum or difference of powers of two Pell numbers
- Some results on certain types of Putcha semigroups
- Inner functions in QK spaces and multipliers
- Certain subclasses of meromorphic multivalent q-starlike and q-convex functions
- Algebraic dependences of meromorphic mappings into a projective space sharing few hyperplanes
- Unbounded oscillation criteria for fourth order neutral differential equations of non-canonical type
- Existence of radial solutions for a weighted p-biharmonic problem with navier boundary condition on the Heisenberg group
- Intuitionistic fuzzy Tribonacci I-convergent sequence spaces
- Lipschitz class functions and their general Fourier coefficients
-
Spectra and fine spectra of the generalized upper difference operator with triple repetition
- A Topological sphere theorem for contact CR-warped product submanifolds of an odd-dimensional unit sphere
- An extended type I half-logistic family of distributions: Properties, applications and different method of estimations
- On the Unit-Chen distribution with associated quantile regression and applications
- A note on Lévy subordinators in cones of fuzzy sets in Banach spaces
- Uniformly asymptotic normality of the weighted estimator in nonparametric regression model with φ-mixing errors
- Upper bound for variance of finite mixtures of power exponential distributions
- The dimension Dind of finite topological T0-spaces
Articles in the same Issue
- Regular Papers
- The poset of morphism-extension classes of countable graphs
- Characterization of monadic BL-algebras by state operators
- Comments on efficient batch verification test for digital signatures based on elliptic curves
- On necessary and sufficient conditions for the monogeneity of a certain class of polynomials
- An exponential Diophantine equation involving the sum or difference of powers of two Pell numbers
- Some results on certain types of Putcha semigroups
- Inner functions in QK spaces and multipliers
- Certain subclasses of meromorphic multivalent q-starlike and q-convex functions
- Algebraic dependences of meromorphic mappings into a projective space sharing few hyperplanes
- Unbounded oscillation criteria for fourth order neutral differential equations of non-canonical type
- Existence of radial solutions for a weighted p-biharmonic problem with navier boundary condition on the Heisenberg group
- Intuitionistic fuzzy Tribonacci I-convergent sequence spaces
- Lipschitz class functions and their general Fourier coefficients
-
Spectra and fine spectra of the generalized upper difference operator with triple repetition
- A Topological sphere theorem for contact CR-warped product submanifolds of an odd-dimensional unit sphere
- An extended type I half-logistic family of distributions: Properties, applications and different method of estimations
- On the Unit-Chen distribution with associated quantile regression and applications
- A note on Lévy subordinators in cones of fuzzy sets in Banach spaces
- Uniformly asymptotic normality of the weighted estimator in nonparametric regression model with φ-mixing errors
- Upper bound for variance of finite mixtures of power exponential distributions
- The dimension Dind of finite topological T0-spaces
