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A sharp maximal inequality for one-dimensional Dunkl martingales

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  • Osȩkowski, Adam

Abstract

Let X=(Xt)t≥0 be a one-dimensional Dunkl process of parameter k≥0, starting from 0. For any p≥1, we find the least constant Cp,k∈(0,∞] in the Doob-type inequality E(sup0≤t≤τXτ)p≤Cp,kE∣Xτ∣p where τ runs over all p/2-integrable stopping times of X. The proof exploits optimal stopping techniques.

Suggested Citation

  • Osȩkowski, Adam, 2015. "A sharp maximal inequality for one-dimensional Dunkl martingales," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 114-119.
    • Handle: RePEc:eee:stapro:v:105:y:2015:i:c:p:114-119
    DOI: 10.1016/j.spl.2015.06.008
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    References listed on IDEAS

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    1. Pedersen, Jesper Lund, 2000. "Best Bounds in Doob's Maximal Inequality for Bessel Processes," Journal of Multivariate Analysis, Elsevier, vol. 75(1), pages 36-46, October.
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