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Sharp Lorentz-norm estimates for BMO martingales

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  • Kamiński, Łukasz
  • Osękowski, Adam

Abstract

Let X be a BMO martingale with continuous paths and let 2≤q≤p<∞ be given parameters. The paper contains the proof of the Lorentz-norm inequality ‖X∞‖p,q≤2−1∕pp∕q(q+1)∕qΓ(q+1)1∕q‖X‖BMO,and the constant is shown to be the best possible.

Suggested Citation

  • Kamiński, Łukasz & Osękowski, Adam, 2021. "Sharp Lorentz-norm estimates for BMO martingales," Statistics & Probability Letters, Elsevier, vol. 173(C).
    • Handle: RePEc:eee:stapro:v:173:y:2021:i:c:s0167715221000304
    DOI: 10.1016/j.spl.2021.109068
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    References listed on IDEAS

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    1. Martin Schweizer & Christophe Stricker & Freddy Delbaen & Pascale Monat & Walter Schachermayer, 1997. "Weighted norm inequalities and hedging in incomplete markets," Finance and Stochastics, Springer, vol. 1(3), pages 181-227.
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