Moment Inequality for the Martingale Square Function
Adam Osękowski
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 61 (2013), p. 169-180 / Harvested from The Polish Digital Mathematics Library
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Consider the sequence (Cₙ)n≥1 of positive numbers defined by C₁ = 1 and Cn+1=1+Cₙ²/4, n = 1,2,.... Let M be a real-valued martingale and let S(M) denote its square function. We establish the bound |Mₙ|≤ Cₙ Sₙ(M), n=1,2,..., and show that for each n, the constant Cₙ is the best possible.

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:281152 
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     title = {Moment Inequality for the Martingale Square Function},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
     volume = {61},
     year = {2013},
     pages = {169-180},
     zbl = {1302.60072},
     language = {en},
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Adam Osękowski. Moment Inequality for the Martingale Square Function. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 61 (2013) pp. 169-180. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba61-2-11/