XIII: 26, 294-306, LNM 721 (1979)
BONAMI, Aline;
LÉPINGLE, Dominique
Fonction maximale et variation quadratique des martingales en présence d'un poids (
Martingale theory)
Weighted norm inequalities in martingale theory assert that a martingale inequality---relating under the law $
P$ two functionals of a $
P$-martingale---remains true, possibly with new constants, when $
P$ is replaced by an equivalent law $Z.
P$. To this order, the ``weight'' $Z$ must satisfy special conditions, among which a probabilistic version of Muckenhoupt's (1972) $(A_p)$ condition and a condition of multiplicative boundedness on the jumps of the martingale $E[Z\,|\,{\cal F}_t]$. This volume contains three papers on weighted norms inequalities,
1326,
1327,
1328, with considerable overlap. Here the main topic is the weighted-norm extension of the Burkholder-Gundy inequalities
Comment: Recently (1997) weighted norm inequalities have proved useful in mathematical finance
Keywords: Weighted norm inequalities,
Burkholder inequalitiesNature: Original
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