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On Fefferman and Burkholder–Davis–Gundy inequalities for ℰ-martingales
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  • Published: March 1999

On Fefferman and Burkholder–Davis–Gundy inequalities for ℰ-martingales

  • Tahir Choulli1,
  • Christoph Stricker1 &
  • Leszek Krawczyk2 

Probability Theory and Related Fields volume 113, pages 571–597 (1999)Cite this article

  • 277 Accesses

  • 11 Citations

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Abstract

In a previous paper we introduced a new concept, the notion of ℰ-martingales and we extended the well-known Doob inequality (for 1 < p < + ∞) and the Burkholder–Davis–Gundy inequalities (for p = 2) to ℰ-martingales. After showing new Fefferman-type inequalities that involve sharp brackets as well as the space bmo q , we extend the Burkholder–Davis–Gundy inequalities (for 1 < p < + ∞) to ℰ-martingales. By means of these inequalities we give sufficient conditions for the closedness in L p of a space of stochastic integrals with respect to a fixed ℝd-valued semimartingale, a question which arises naturally in the applications to financial mathematics. Finally we investigate the relation between uniform convergence in probability and semimartingale topology.

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Authors and Affiliations

  1. Laboratoire de Mathématiques, UMR CNRS 6623, 16 Route de Gray, F-25030 Besançon Cedex, France. e-mail: tahir@math.univ-fcomte.fr; stricker@math.univ-fcomte.fr, , , , , , FR

    Tahir Choulli & Christoph Stricker

  2. Department of Mathematics, Warsaw University, Banacha 2, PL-02-097 Warsaw, Poland. e-mail: krawczyk@mimuw.edu.pl, , , , , , PL

    Leszek Krawczyk

Authors
  1. Tahir Choulli
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  2. Christoph Stricker
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  3. Leszek Krawczyk
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Received: 22 July 1997 / Revised version: 3 July 1998

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Choulli, T., Stricker, C. & Krawczyk, L. On Fefferman and Burkholder–Davis–Gundy inequalities for ℰ-martingales. Probab Theory Relat Fields 113, 571–597 (1999). https://doi.org/10.1007/s004400050218

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  • Issue Date: March 1999

  • DOI: https://doi.org/10.1007/s004400050218

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  • Mathematics Subject classification (1991): 60G48, 60H05, 90A09
  • Keywords: Semimartingales, Semimartingale topology, Stochastic integrals, Stochastic Exponential, Fefferman inequality, Burkholder–Davis–Gundy inequality.
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