Duality and quasy-continuity for supermartingales

Abstract.

Considering the ordered convex cone $\cal{S}$ of all positive right continuous supermartingales, we give a complete description of its dual. Also we study quasi-boundedness, quasi-continuity ans substractivity in $\cal{S}$, proving that: the universally quasi-bounded potentials are exactly the potentials of class (D), the quasi-continuous potentials are exactly the regular potentials of class (D), and the substractible elements are exactly the local martingales.

Keywords: supermantigale, increasing process, (predictable) stopping time, Riesz decomposition property, duality