Sankhya: The Indian Journal of Statistics

1993, Volume 55, Series A, Pt. 1, 12-28

CESÁRO UNIFORM INTEGRABILITY AND LP-CONVERGENCE

By

ARUP BOSE, Purdue University

And

TAPAS K. CHANDRA, Indian Statistical Institute

 

SUMMARY. We show how a new condition, called Cesàro uniform integrability, introduced by Chandra (1989) can be

used in many cases to prove Lp-convergence of n-1/p Sn where Sn = $\sigma^n_(i=0)$Xi.

AMS (1985) subject classification. 60F25,60G48,60G50

Key words and phrases. Cesaro uniform integrability, $L_p$-convergence, martingale differences, $L_p$-mixingale differences, autoregressive process, moving average process

FULL PAPER.

This article in Mathematical Reviews.