On a Convex Function Inequality for Martingales
Garsia, Adriano M.
Ann. Probab., Tome 1 (1973) no. 5, p. 171-174 / Harvested from Project Euclid
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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 $\Phi(2u) \leqq c\Phi(u)$.
Publié le : 1973-02-14
Classification:  26-A51,  Martingales,  convex,  convex function inequalities for martingales,  60G45 
@article{1176997032,
     author = {Garsia, Adriano M.},
     title = {On a Convex Function Inequality for Martingales},
     journal = {Ann. Probab.},
     volume = {1},
     number = {5},
     year = {1973},
     pages = { 171-174},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176997032}
}

Garsia, Adriano M. On a Convex Function Inequality for Martingales. Ann. Probab., Tome 1 (1973) no. 5, pp.  171-174. http://gdmltest.u-ga.fr/item/1176997032/