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XIII: 39, 453-471, LNM 721 (1979)
YOR, Marc
Sur le balayage des semi-martingales continues (General theory of processes)
For the general notation, see 1338. This paper is independent from the preceding one 1338, and some overlap occurs. The balayage formula is extended to processes $Z$ which are not locally bounded, and the local time of the semimartingale $Y$ is computed. The class of continuous semimartingales $X$ with canonical decomposition $X=M+V$ such that $dV$ is carried by $H=\{X=0\}$ is introduced and studied. It turns out to be an important class, closely related to relative martingales'' (Azéma, Meyer and Yor 2623). A number of results are given, too technical to be stated here. Stopping previsible, optional and progressive processes at the last exit time $L$ from $H$ leads to three $\sigma$-fields, ${\cal F}_L^p$, ${\cal F}_L^o$, ${\cal F}_L^{\pi}$, and it was considered surprising that the last two could be different (see 1240). Here it is shown that if $X$ is a continuous uniformly integrable martingale with $X_0=0$, $E[X_{\infty}|{\cal F}_L^o]=0\neq E[X_{\infty}|{\cal F}_L^{\pi}]$
Comment: See 1357
Keywords: Local times, Balayage, Balayage formula
Nature: Original
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