Holderian weak invariance principle under a Hannan type condition

被引：6
|
作者：
Giraudo, Davide [1 ]
机构：
[1] Univ Rouen, LMRS, F-76801 St Etienne, France
来源：
STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2016年 / 126卷 / 01期
关键词：
Invariance principle; Martingales; Strictly stationary process; CENTRAL LIMIT-THEOREMS;
D O I：
10.1016/j.spa.2015.09.001
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We investigate the invariance principle in Holder spaces for strictly stationary martingale difference sequences. In particular, we show that the sufficient condition on the tail in the i.i.d. case does not extend to stationary ergodic martingale differences. We provide a sufficient condition on the conditional variance which guarantee the invariance principle in Holder spaces. We then deduce a condition in the spirit of Hannan one. (C) 2015 Elsevier B.V All rights reserved.
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页码：290 / 311
页数：22
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