Geodesic
Sharp Norm Inequalities for Martingales and their Differential Subordinates
Adam Os/ekowski1
1 Department of Mathematics, Informatics and Mechanics Warsaw University Banacha 2 02-097 Warszawa, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) no. 4, pp. 373-385

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

Suppose $f=(f_n)$, $g=(g_n)$ are martingales with respect to the same filtration, satisfying $$ |f_n-f_{n-1}| \leq |g_n-g_{n-1}|,\quad \ n=1,2,\ldots, $$ with probability $1$. Under some assumptions on $f_0$, $g_0$ and an additional condition that one of the processes is nonnegative, some sharp inequalities between the $p$th norms of $f$ and $g$, $0 p \infty$, are established. As an application, related sharp inequalities for stochastic integrals and harmonic functions are obtained.
DOI : 10.4064/ba55-4-9
Keywords: suppose martingales respect filtration satisfying n f n leq n g n quad ldots probability under assumptions additional condition processes nonnegative sharp inequalities between pth norms infty established application related sharp inequalities stochastic integrals harmonic functions obtained

Adam Os/ekowski 1

1 Department of Mathematics, Informatics and Mechanics Warsaw University Banacha 2 02-097 Warszawa, Poland 
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Adam Os/ekowski. Sharp Norm Inequalities for Martingales and their
 Differential Subordinates. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) no. 4, pp. 373-385. doi: 10.4064/ba55-4-9

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