We consider quasi-martingales indexed by a linearly order set. We show that such processes are isomorphic to a given class of (finitely additive) measures. From this result we easily derive the classical theorem of Stricker as well as the decompositions of Riesz, Rao and the supermartingale decomposition of Doob and Meyer.
Cassese, G. (2010). Quasimartingales with a Linearly Ordered Index Set. STATISTICS & PROBABILITY LETTERS, 80(5-6), 421-426 [10.1016/j.spl.2009.11.019].
Quasimartingales with a Linearly Ordered Index Set
CASSESE, GIANLUCA
2010
Abstract
We consider quasi-martingales indexed by a linearly order set. We show that such processes are isomorphic to a given class of (finitely additive) measures. From this result we easily derive the classical theorem of Stricker as well as the decompositions of Riesz, Rao and the supermartingale decomposition of Doob and Meyer.
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