DOOB’S DECOMPOSITION OF FUZZY SUBMARTINGALES VIA ORDERED NEAR VECTOR SPACES - Labuschagne, C. C. A.; Pinchuck, A. L. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2011)
We use ideas from measure-freemartin gale theory and a near vector space to derive a Doob decomposition of submartingalesin ordered near vector spaces, which is a generalization of result noted by Daures, Ni and Zhang, and an analogue of the Doob decomposition of submartingales in the fuzzy setting, as noted by Shen and Wang.