# zbMATH — the first resource for mathematics

Some properties of the accessible field; the discontinuities of an integrable crossing process and the discontinuities of its dual predictable projection. (Quelques propriétés de la tribu accessible; les discontinuités d’un processus croissant intégrable et les discontinuités de sa projection prévisible duale.) (French) Zbl 0747.60040
Séminaire de probabilités XXIII, Lect. Notes Math. 1372, 355-361 (1989).
[For the entire collection see Zbl 0722.00030.]
Let $$X$$ be a special semimartingale and let $$X=M+X^ \natural$$ be its decomposition into a local martingale $$M$$ and a predictable process of finite variation $$X^ \natural$$. Let $$A$$ be the set of accessible discontinuities of $$X$$, $$\overline A$$ its predictable envelope, and let $$A^ \natural$$ be the predictable set of the discontinuities of $$X^ \natural$$. The author shows that $$A^ \natural\subset\overline A$$ and, if $$X$$ is increasing, that $$A^ \natural=\overline A$$. Moreover, he gives the optional, the predictable and the accessible desintegration of the underlying probability measure.
Reviewer: M.Dozzi (Ittigen)
##### MSC:
 60G17 Sample path properties 60G07 General theory of stochastic processes
Full Text: