Open Access
Translator Disclaimer
February, 1973 On a Convex Function Inequality for Martingales
Adriano M. Garsia
Ann. Probab. 1(1): 171-174 (February, 1973). DOI: 10.1214/aop/1176997032

Abstract

A new proof is given for the inequality $$E(\Phi(\Sigma^\infty_{\nu=1} E(z_\nu \mid \mathscr{F}_\nu))) \leqq CE(\Phi(\Sigma^\infty_{\nu=1} z_\nu)),$$ where $z_1, z_2, \cdots, z_n, \cdots$ are nonnegative random variables on a probability space $(\Omega, \mathscr{F}, \mathbf{P}), \mathscr{F}_1 \subset \mathscr{F}_2 \subset \cdots \subset \mathscr{F}_n \subset \cdots \mathscr{F}$ is a sequence of $\sigma$-fields and $\Phi(u)$ is a convex function satisfying $\Phi(2u) \leqq c\Phi(u)$.

Citation

Download Citation

Adriano M. Garsia. "On a Convex Function Inequality for Martingales." Ann. Probab. 1 (1) 171 - 174, February, 1973. https://doi.org/10.1214/aop/1176997032

Information

Published: February, 1973
First available in Project Euclid: 19 April 2007

zbMATH: 0289.60026
MathSciNet: MR346897
Digital Object Identifier: 10.1214/aop/1176997032

Subjects:
Primary: 60G45

Keywords: 26-A51 , convex , convex function inequalities for martingales , Martingales

Rights: Copyright © 1973 Institute of Mathematical Statistics

JOURNAL ARTICLE
4 PAGES


SHARE
Vol.1 • No. 1 • February, 1973
Back to Top