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Zbl 0814.60039
Jacod, J.; Skorohod, A.V.
(Skorokhod, A. V.)
Jumping filtrations and martingales with finite variation. (English)
[A] Azéma, Jacques (ed.) et al., Séminaire de Probabilités XXVIII. Berlin: Springer-Verlag. Lect. Notes Math. 1583, 21-35 (1994). ISBN 3-540-58331-9/pbk

In contrast with Brownian filtrations, the so-called jumping filtrations are locally constant between the successive occurrences of an increasing sequence of stopping times. The authors prove that a filtration is a jumping one if and only if all its martingales have locally finite variation. The necessary condition is easy, and as well the sufficient condition if moreover the filtration is quasi-left continuous; the proof is more intricate in the general case and requires some use of integration with respect to random measures.
[D.Lepingle (Orléans)]

MSC 2000:: *60G44 Martingales with continuous parameter

Keywords: stochastic integrals; jumping filtrations; locally finite variation; random measures

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