Systèmes de sortie \(({\mathcal F}_{D_ t})\) prévisibles. (\(({\mathcal F}_{D_ t})\)-predictable exit systems) (Q1113210)

Consider a random closed set which is adapted to a filtration (\({\mathcal F}_ t)\). Define \(D_ t=\inf \{s>t:\) \(s\in M\}\). The author defines a local time of M which is adapted to (\({\mathcal F}_ t)\) and is also (\({\mathcal F}_{D_ t})\) predictable. Furthermore, an exit system is associated with M and the process representing the future at time t, which is both (\({\mathcal F}_ t)\) optional and (\({\mathcal F}_{D_ t})\) predictable. The general results are applied to Ray processes.