XVI: 26, 298-313, LNM 920 (1982)
DELLACHERIE, Claude;
LENGLART, Érik
Sur des problèmes de régularisation, de recollement et d'interpolation en théorie des processus (
General theory of processes)
This paper is a sequel to
1524. Let $\Theta$ be a
chronology, i.e., a family of stopping times containing $0$ and $\infty$ and closed under the operations $\land,\lor$---examples are the family of all stopping times, and that of all deterministic stopping times. The general problem discussed is that of defining an optional process $X$ on $[0,\infty]$ such that for each $T\in\Theta$ $X_T$ is a.s. equal to a given r.v. (${\cal F}_T$-measurable). While in
1525 the discussion concerned supermartingales, it is extended here to processes which satisfy a semi-continuity condition from the right
Keywords: Stopping timesNature: Original
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