Geodesic
A Weak-Type Inequality for Submartingales and Itô Processes
Adam Osękowski1
1 Department of Mathematics, Informatics and Mechanics University of Warsaw Banacha 2 02-097 Warszawa, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015) no. 1, pp. 73-88

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let $\alpha\in [0,1]$ be a fixed parameter. We show that for any nonnegative submartingale $X$ and any semimartingale $Y$ which is $\alpha$-subordinate to $X$, we have the sharp estimate $$ \|Y\|_{W}\leq \frac{2(\alpha+1)^2}{2\alpha+1}\|X\|_{L^\infty}.$$ Here $W$ is the weak-$L^\infty$ space introduced by Bennett, DeVore and Sharpley. The inequality is already sharp in the context of $\alpha$-subordinate It\^o processes.
DOI : 10.4064/ba63-1-9
Keywords: alpha fixed parameter nonnegative submartingale semimartingale which alpha subordinate have sharp estimate leq frac alpha alpha infty here weak l infty space introduced bennett devore sharpley inequality already sharp context alpha subordinate processes

Adam Osękowski 1

1 Department of Mathematics, Informatics and Mechanics University of Warsaw Banacha 2 02-097 Warszawa, Poland 
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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) no. 1, pp. 73-88. doi: 10.4064/ba63-1-9

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