A Weak-Type Inequality for Submartingales and Itô Processes
Adam Osękowski
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015), p. 73-88 / Harvested from The Polish Digital Mathematics Library
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Let α ∈ [0,1] be a fixed parameter. We show that for any nonnegative submartingale X and any semimartingale Y which is α-subordinate to X, we have the sharp estimate ∥Y∥W≤(2(α+1)²)/(2α+1)∥X∥L∞. Here W is the weak-L∞ space introduced by Bennett, DeVore and Sharpley. The inequality is already sharp in the context of α-subordinate Itô processes.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:281306 
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Adam Osękowski. A Weak-Type Inequality for Submartingales and Itô Processes. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015) pp. 73-88. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba63-1-9/