ON THE TESTING MULTI-VALUED MARTINGALE DIFFERENCE HYPOTHESIS

This paper presents a definition of Multi-Valued Martingale Difference (MVMD) based on Castaing representation of a multi-valued martingale that consists of martingale difference selections. Testing the Multi-Valued Martingale Difference Hypothesis (MVMDH) then examined. Testing the Martingale Difference Hypothesis (MDH) earlier was based on linear measures then later developed two directions in order to account for the existing nonlinearity in economic and financial data. First, the classical approaches have been modified by take into account the possible nonlinear dependence. Second, the use of more sophisticated statistical tools such as those based generalized spectral analysis. According to this article, both these developments in MDH are modified for MVMDH and applies them to exchange rate data and returns of stock market data.

On representation of multimeasure

We consider a multimeasure with the Radon-Nikodym derivative and apply its Castaing representation to get a representation of the multimeasure.

On the Integrable Solution of a Class of Fuzzy Functional Equations

This paper proves the existence of Lp solution to the fuzzy functional equation [Formula: see text] where a and y are fuzzy functions and h is a given deterministic function. This functional equation is fuzzified using Zadeh's extension principle and the existence theorem is proved using the contraction principle, Castaing representation theorem and Negoita and Ralescu's representation theorem. This supplements and earlier existence theorem we obtained for bounded fuzzy solutions.