Abstract
On a probability space (ΩℱP), a filtration (ℱt)t≥0 is called a jumping filtration if there is a sequence (Tn) of stopping times increasing to +∞, such that on each set {Tn≤t<Tn+1 the σ-fields ℱt and \(\mathfrak{F}_{T_n }\) coincide up to null sets. The main result is that (ℱt) is a jumping filtration iff all martingales have a.s. locally finite variation.
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Reference
J. JACOD: Calcul stochastique et problèmes de martingales. Lect. Notes in Math., 714. Springer Verlag: Berlin, 1979.
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© 1994 Springer-Verlag
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Jacod, J., Skorohod, A.V. (1994). Jumping filtrations and martingales with finite variation. In: Azéma, J., Yor, M., Meyer, P.A. (eds) Séminaire de Probabilités XXVIII. Lecture Notes in Mathematics, vol 1583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073831
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DOI: https://doi.org/10.1007/BFb0073831
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