Reducing non-stationary stochastic processes to stationarity by a time deformation

被引：27

作者：

Perrin, O ^{[1
]}

Senoussi, R ^{[1
]}

机构：

[1] INRA, F-84914 Avignon 9, France

来源：

STATISTICS & PROBABILITY LETTERS | 1999年 / 43卷 / 04期

关键词：

correlation function; stationary reducibility; weak stationarity;

D O I：

10.1016/S0167-7152(98)00278-8

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：

A necessary and sufficient condition is given to reduce a non-stationary random process {Z(t): t is an element of T subset of or equal to R} to stationarity via a bijective differentiable time deformation Phi so that its correlation function r(t,t') depends only on the difference Phi(t') - Phi(t) through a stationary correlation function R: r(t,t') = R(Phi(t') - Phi(t)). (C) 1999 Elsevier Science B.V. All rights reserved.

引用

页码：393 / 397

页数：5

共 50 条

[1] On a time deformation reducing nonstationary stochastic processes to local stationarity
Genton, MG
Perrin, O
[J]. JOURNAL OF APPLIED PROBABILITY, 2004, 41 (01) : 236 - 249
[2] Reducing non-stationary random fields to stationarity and isotropy using a space deformation
Perrin, O
Senoussi, R
[J]. STATISTICS & PROBABILITY LETTERS, 2000, 48 (01) : 23 - 32
[3] Martingale approximation of non-stationary stochastic processes
Volny, Dalibor
[J]. STOCHASTICS AND DYNAMICS, 2006, 6 (02) : 173 - 183
[4] THE SHIFT OPERATOR FOR NON-STATIONARY STOCHASTIC PROCESSES
GETOOR, RK
[J]. DUKE MATHEMATICAL JOURNAL, 1956, 23 (01) : 175 - 187
[5] Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting
Liu, Yong
Wu, Haixu
Wang, Jianmin
Long, Mingsheng
[J]. ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 35 (NEURIPS 2022), 2022,
[6] A stochastic harmonic function representation for non-stationary stochastic processes
Chen, Jianbing
Kong, Fan
Peng, Yongbo
[J]. MECHANICAL SYSTEMS AND SIGNAL PROCESSING, 2017, 96 : 31 - 44
[7] PHYSICAL INTERPRETATION OF SPECTRA OF NON-STATIONARY STOCHASTIC PROCESSES
PRIESTLEY, MB
[J]. JOURNAL OF SOUND AND VIBRATION, 1971, 17 (01) : 51 - +
[8] Non-stationary stochastic multi-armed bandit problems with external information on stationarity
Namba, Hiroyuki
[J]. Transactions of the Japanese Society for Artificial Intelligence, 2021, 36 (03):
[9] Random function based spectral representation of stationary and non-stationary stochastic processes
Liu, Zhangjun
Liu, Wei
Peng, Yongbo
[J]. PROBABILISTIC ENGINEERING MECHANICS, 2016, 45 : 115 - 126
[10] SPECTRAL ANALYSIS OF CONVOLUTION AND FILTERING OF NON-STATIONARY STOCHASTIC PROCESSES
MARK, WD
[J]. JOURNAL OF SOUND AND VIBRATION, 1970, 11 (01) : 19 - &

← 1 2 3 4 5 →