Osȩkowski, Adam - In: Statistics & Probability Letters 95 (2014) C, pp. 139-143
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,λ0, involving the one-sided maximal function on the right-hand side. The constant e is the...