I have a sequence of random variables $X_1, X_2, \ldots X_N$ such that $|X_i| \leq R \ \forall \ i $, satisfying $$|E[X_n|X_1,X_2,\ldots X_{n-1}]| \leq |X_{n-1}|, $$
Can I construct a sub/super-martingale sequence from this? Intuitively, it makes sense that the random variables are constrained to be not from far the previous one in absolute/distance sense. But can I view this as some sort of martingale or perhaps construct a sequence (or sequences) which satisfy the definition of (sub/super)martingale(s)?