Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1151680 | Statistics & Probability Letters | 2014 | 5 Pages |
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Adam Osȩkowski,