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April, 1975 Deux Inegalites Concernant Les Operateurs de Burkholder Sur Les Martingales
Maurizio Pratelli
Ann. Probab. 3(2): 365-370 (April, 1975). DOI: 10.1214/aop/1176996409

Abstract

In this paper the following two theorems are shown: if $U, V$ are Burkholder type operators on martingales and if the inequality $E\lbrack U(X) \rbrack \leqq c \cdot E\lbrack V(X) \rbrack$ holds for every martingale $X$, then the inequality $E\lbrack F \circ U(X) \rbrack \leqq C \cdot E\lbrack F \circ V(X) \rbrack$ holds, for $F$ concave if $V$ is "predictable," for $F$ convex if $U$ is "predictable."

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Maurizio Pratelli. "Deux Inegalites Concernant Les Operateurs de Burkholder Sur Les Martingales." Ann. Probab. 3 (2) 365 - 370, April, 1975. https://doi.org/10.1214/aop/1176996409

Information

Published: April, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0303.60041
MathSciNet: MR372991
Digital Object Identifier: 10.1214/aop/1176996409

Subjects:
Primary: 60G45
Secondary: 47H99

Keywords: Burkholder operators , Convex functions , Inequalities‎ , Martingales , stopping times

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 2 • April, 1975
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