Abstract
Abstract Martingales are a class of stochastic processes which has had profound influence on the development of probability theory and stochastic processes. Some recent developments are related to mathematical finance. In the real world, some information about these phenomena might be imprecise and represented in the form of vague quantities. In these situations, we need to generalize classical methods to vague environment. Thus, fuzzy martingales have been extended as a vague perception of real-valued martingales. In this paper, some moment inequalities are presented for fuzzy martingales. Several convergence theorems are established based on these inequalities. As an application of convergence theorems, a weak law of large numbers for fuzzy martingales is stated. Furthermore, a few examples are devoted to clarify the main results.
Highlights
Over the last decades, the theory of fuzzy random variables has been extensively developed
Klement et al [6] established a strong law of large numbers for fuzzy random variables, based on embedding theorem as well as certain probability techniques in the Banach spaces
Taylor et al [7] proved a weak law of large numbers for fuzzy random variables in separable Banach spaces
Summary
The theory of fuzzy random variables has been extensively developed. Klement et al [6] established a strong law of large numbers for fuzzy random variables, based on embedding theorem as well as certain probability techniques in the Banach spaces. Some moment inequalities for fuzzy martingales are established and convergence theorems of such fuzzy random variables are studied.
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