Quasimartingales with a linearly ordered index set

Gianluca Cassese

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.

Mots clés: primary 28A12; 60G07; 60G20

Gianluca Cassese. Quasimartingales with a linearly ordered index set. Statistics and Probability Letters, 2010, 80 (5-6), pp.421. ⟨10.1016/j.spl.2009.11.019⟩. ⟨hal-00612016⟩