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XII: 30, 425-427, LNM 649 (1978)
DELLACHERIE, Claude; MEYER, Paul-André
Construction d'un processus prévisible ayant une valeur donnée en un temps d'arrêt (General theory of processes)
Let $T$ be a stopping time, $X$ be an integrable r.v., and put $A_t=I_{\{t\ge T\}}$ and $B_t=XA_t$. Then the previsible compensator $(\tilde B_t)$ has a previsible density $Z_t$ with respect to $(\tilde A_t)$, whose value $Z_T$ at time $T$ is $E[X\,|\,{\cal F}_{T-}]$, and in particular if $X$ is ${\cal F}_T$-measurable it is equal to $X$
Keywords: Stopping times
Nature: Original
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