XIII: 40, 472-477, LNM 721 (1979)
STRICKER, Christophe
Semimartingales et valeur absolue (General theory of processes)
For the general notation, see 1338. A result of Yoeurp that absolute values preserves quasimartingales is extended: convex functions satisfying a Lipschitz condition operate on quasimartingales. For $p\ge1$, $X\in H^p$ implies $|X|^p\in H^1$. Then it is shown that for a continuous adapted process $X$, it is equivalent to say that $X$ and $|X|$ are quasimartingales (or semimartingales). Then comes a result related to the main problem of this series: with the general notations above, if $X$ is assumed to be a quasimartingale such that $X_{D_t}=0$ for all $t$, if the process $Z$ is progressive and bounded, then the process $Z_{g_t}X_t$ is a quasimartingale
Comment: A complement is given in the next paper 1341. See also 1351
Keywords: Balayage, Quasimartingales
Nature: Original
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