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

Schwartz, Laurent

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

Keywords:

semimartingale; decomposition; predictable set of the discontinuities; desintegration

Citations:

Zbl 0722.00030