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.

引用

页码：290 / 311

页数：22

共 31 条

[1] Holderian weak invariance principle under the Maxwell and Woodroofe condition [J].

Giraudo, Davide .

BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS, 2018, 32 (01) :172-187

[2] Holderian Weak Invariance Principle for Stationary Mixing Sequences [J].

Davide Giraudo .

Journal of Theoretical Probability, 2017, 30 :196-211

[3] Holderian Weak Invariance Principle for Stationary Mixing Sequences [J].

Giraudo, Davide .

JOURNAL OF THEORETICAL PROBABILITY, 2017, 30 (01) :196-211

[4] An invariance principle for stationary random fields under Hannan's condition [J].

Volny, Dalibor ;

Wang, Yizao .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2014, 124 (12) :4012-4029

[5] Holderian invariance principle for linear processes [J].

Juodis, Mindaugas ;

Rackauskas, Alfredas ;

Suquet, Charles .

ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2009, 5 :47-64

[6] Weak invariance principle for integral-type functionals [J].

Szyszkowski, I .

THEORY OF PROBABILITY AND ITS APPLICATIONS, 1997, 41 (01) :185-192

[7] On the weak invariance principle for non-adapted stationary random fields under projective criteria [J].

Lin, Han-Mai .

STOCHASTICS AND DYNAMICS, 2022, 22 (05)

[8] Invariance principle in a bilinear model with weak nonlinearity [J].

Lifshits M.A. .

Journal of Mathematical Sciences, 2006, 137 (1) :4541-4545

[9] A NEW CONDITION FOR THE INVARIANCE PRINCIPLE FOR STATIONARY RANDOM FIELDS [J].

Wang, Yizao ;

Woodroofe, Michael .

STATISTICA SINICA, 2013, 23 (04) :1673-1696

[10] An estimator of the number of change points based on a weak invariance principle [J].

Kühn, C .

STATISTICS & PROBABILITY LETTERS, 2001, 51 (02) :189-196

← 1 2 3 4 →