The Annals of Probability

Deux Inegalites Concernant Les Operateurs de Burkholder Sur Les Martingales

Maurizio Pratelli

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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."

Article information

Source
Ann. Probab., Volume 3, Number 2 (1975), 365-370.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996409

Digital Object Identifier
doi:10.1214/aop/1176996409

Mathematical Reviews number (MathSciNet)
MR372991

Zentralblatt MATH identifier
0303.60041

JSTOR
links.jstor.org

Subjects
Primary: 60G45
Secondary: 47H99: None of the above, but in this section

Keywords
Martingales Burkholder operators inequalities convex functions stopping times

Citation

Pratelli, Maurizio. Deux Inegalites Concernant Les Operateurs de Burkholder Sur Les Martingales. Ann. Probab. 3 (1975), no. 2, 365--370. doi:10.1214/aop/1176996409. https://projecteuclid.org/euclid.aop/1176996409


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