Moment Inequalities for Sums of Dependent Random Variables under Projective Conditions |
| |
Authors: | Emmanuel Rio |
| |
Affiliation: | (1) UMR 8100 CNRS—Laboratoire de mathématiques de Versailles, Bat. Fermat, 45 Avenue des Etats Unis, 78035 Versailles Cedex, France |
| |
Abstract: | We obtain precise constants in the Marcinkiewicz-Zygmund inequality for martingales in for p>2 and a new Rosenthal type inequality for stationary martingale differences for p in ]2,3]. The Rosenthal inequality is then extended to stationary and adapted sequences. As in Peligrad et al. (Proc. Am. Math. Soc. 135:541–550, [2007]), the bounds are expressed in terms of -norms of conditional expectations with respect to an increasing field of sigma algebras. Some applications to a particular Markov chain are given. |
| |
Keywords: | Martingale Moment inequality Stationary sequences Projective criteria Rosenthal inequality |
本文献已被 SpringerLink 等数据库收录! |
|