Article ID Journal Published Year Pages File Type
1151680 Statistics & Probability Letters 2014 5 Pages PDF
Abstract

Let f=(fn)n≥0f=(fn)n≥0 be a real-valued martingale satisfying f0≥0f0≥0 almost surely and let S(f)S(f) denote the square function of ff. 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 ee is the best possible.

Related Topics
Physical Sciences and Engineering Mathematics Statistics and Probability
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