Doob's Decomposition Theorem for Fuzzy (Super) Submartingales

Abstract

The notions of fuzzy random variables and fuzzy (super) submartingales are introduced. In this paper we provide the necessary and sufficient conditions of Doob's decomposition for fuzzy (super) submartingales. Finally, we discuss the decomposition of fuzzy (super) submartingales on R, and an example is given which explains that not every fuzzy (super) submartingale has Doob's decomposition.