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Jumping filtrations and martingales with finite variation

Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 1583)

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.

Keywords

  • Random Measure
  • Polish Space
  • Stochastic Integral
  • Local Martingale
  • Finite Variation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Reference

  1. 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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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58331-8

  • Online ISBN: 978-3-540-48656-5

  • eBook Packages: Springer Book Archive