A weak-type inequality for the martingale square function

Adam Osȩkowski

Statistics & Probability Letters, 2014, vol. 95, issue C, 139-143

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.

Keywords: Square function; Martingale; Weak-type inequality; Best constant (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1016/j.spl.2014.08.019

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