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A weak-type inequality for the martingale square function

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  • Osȩkowski, Adam

Abstract

Let f=(fn)n≥0 be a real-valued martingale satisfying f0≥0 almost surely and let S(f) denote the square function of f. The paper contains the proof of the weak-type bound λP(S(f)≥λ)≤eEsupn≥0fn,λ>0, involving the one-sided maximal function on the right-hand side. The constant e is the best possible.

Suggested Citation

  • Osȩkowski, Adam, 2014. "A weak-type inequality for the martingale square function," Statistics & Probability Letters, Elsevier, vol. 95(C), pages 139-143.
    • Handle: RePEc:eee:stapro:v:95:y:2014:i:c:p:139-143
    DOI: 10.1016/j.spl.2014.08.019
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