Decomposition theorems for fuzzy supermartingales and submartingales
type: Item
instance of: scholarly article
title: Decomposition theorems for fuzzy supermartingales and submartingales
zbMATH Open document ID: 0966.60042
DOI: 10.1016/S0165-0114(98)00065-7
author: Yuhu Feng
published in: Fuzzy Sets and Systems
publication date: 2001-08-12T00:00:00Z
review text: The aim of this paper is to generalize the Doob decomposition and the Riesz decomposition theorems of standard martingale theory to the case of fuzzy martingales. The fact that the fuzzy number space is not a linear space represents one of the main difficulties to obtain the intended results. In order to overcome this problem. Section 2 gives the representation theorem of fuzzy numbers on the basis of their support functions, and uses the concept of H-difference of fuzzy numbers and its properties. Different measurability concepts for fuzzy random variables, relationships among them, and two counterexamples are discussed. Section 3 studies the Doob decomposition of fuzzy supermartingales and submartingales. Since not all fuzzy supermartingales and submartingales are proved to have Doob decomposition, the author obtains necessary and sufficient conditions for a fuzzy supermartingale (respective submartingale) to provide Doob decomposition. Section 4 is devoted to Riesz decomposition for fuzzy supermartingales. Two notions of Riesz decomposition are defined, and necessary and sufficient conditions for a fuzzy supermartingale to have Riesz decomposition are analyzed.
reviewed by: Neculai Curteanu
Mathematics Subject Classification ID: 60G48
Mathematics Subject Classification ID: 28E10
zbMATH DE Number: 1547847
zbMATH Keywords: fuzzy martingale
zbMATH Keywords: supermartingale
zbMATH Keywords: submartingale
zbMATH Keywords: Doob decomposition
zbMATH Keywords: Riesz decomposition
MaRDI profile type: Publication
cites work: Measurability concepts for fuzzy mappings
cites work: Metric spaces of fuzzy sets
cites work: Convergence theorems for fuzzy random variables and fuzzy martingales
cites work: Gaussian fuzzy random variables
cites work: Q4274285
cites work: On the convergence of fuzzy sets
cites work: Fuzzy differential equations
cites work: Fuzzy random variables
cites work: Convergence theorem for fuzzy martingales
full work available at URL: s0165-0114(98)00065-7
OpenAlex ID: W2071989824
description: scientific article; zbMATH DE number 1547847