Sharp Norm Inequalities for Martingales and their
 Differential Subordinates

Adam Os/ekowski

doi:10.4064/ba55-4-9

Geodesic

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Sharp Norm Inequalities for Martingales and their Differential Subordinates

Adam Os/ekowski ¹

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

Résumé

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

Mots-clés : 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

Affiliations des auteurs :

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. https://geodesic-test.mathdoc.fr/articles/10.4064/ba55-4-9/

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