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Pointwise Properties of Martingales with Values in Banach Function Spaces

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High Dimensional Probability VIII

Part of the book series: Progress in Probability ((PRPR,volume 74))

Abstract

In this paper we consider local martingales with values in a UMD Banach function space. We prove that such martingales have a version which is a martingale field. Moreover, a new Burkholder–Davis–Gundy type inequality is obtained.

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Acknowledgements

The authors would like to thank the referee for helpful comments.

Mark Veraar is supported by the Vidi subsidy 639.032.427 of the Netherlands Organisation for Scientific Research (NWO).

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Authors and Affiliations

  1. Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands

    Mark Veraar & Ivan Yaroslavtsev

Authors
  1. Mark Veraar
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  2. Ivan Yaroslavtsev
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Correspondence to Mark Veraar .

Editor information

Editors and Affiliations

  1. MAP 5, Université Paris Descartes, Paris, France

    Nathael Gozlan

  2. Institute of Mathematics, University of Warsaw, Warsaw, Poland

    Rafał Latała

  3. Centre de Mathématiques Appliquées, Ecole Polytechnique, Palaiseau, France

    Karim Lounici

  4. Department of Mathematical Sciences, University of Delaware, Newark, DE, USA

    Mokshay Madiman

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Veraar, M., Yaroslavtsev, I. (2019). Pointwise Properties of Martingales with Values in Banach Function Spaces. In: Gozlan, N., Latała, R., Lounici, K., Madiman, M. (eds) High Dimensional Probability VIII. Progress in Probability, vol 74. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-26391-1_16

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