Some examples and counterexamples of convergence of σ-algebras and filtrations

We study some properties of the weak convergence of filtrations, in particular, its behavior under elementary set operations. We also derive relations between the convergence of filtrations generated by point processes with a single jump and the convergence of their compensators or distributions of their jump moments. Finally, we apply a lemma on the intersection of σ-algebras to filtrations generated by different discretizations of a single process. © 2000 Kluwer Academic/Plenum Publishers.