A note on processes with random stationary increments

被引：2
作者：
Zhang, Haimeng [1 ]
Huang, Chunfeng [2 ,3 ]
机构：
[1] Univ N Carolina, Dept Math & Stat, Greensboro, NC 27412 USA
[2] Indiana Univ, Dept Stat, Bloomington, IN 47408 USA
[3] Indiana Univ, Dept Geog, Bloomington, IN 47408 USA
来源：
STATISTICS & PROBABILITY LETTERS | 2014年 / 94卷
基金：
美国国家科学基金会;
关键词：
Intrinsic stationarity; Variogram; Spectrum; Structure function; Inversion formula; INTRINSIC RANDOM FUNCTIONS; SELF-SIMILARITY; VARIOGRAM;
D O I：
10.1016/j.spl.2014.07.016
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：
When the correlation theory is considered for the processes with random stationary increments, Yaglom (1955) has developed the spectral representation theory. In this note, we complete this development by obtaining the inversion formula of the spectrum in terms of the structure function. (C) 2014 Elsevier B.V. All rights reserved.
引用
收藏
页码：153 / 161
页数：9
相关论文
共 23 条
[1]  
[Anonymous], 1999, INTERPOLATION SPATIA
[2]   Self-similarity: Part II - Optimal estimation of fractal processes [J].
Blu, Thierry ;
Unser, Michael .
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2007, 55 (04) :1364-1378
[3]  
Brockwell Peter J, 2009, Time Series: Theory and Methods
[4]  
Chiles J.-P., 2012, GEOSTATISTICS MODELI, DOI DOI 10.1002/9781118136188
[5]   ON THE PROBLEM OF PERMISSIBLE COVARIANCE AND VARIOGRAM MODELS [J].
CHRISTAKOS, G .
WATER RESOURCES RESEARCH, 1984, 20 (02) :251-265
[6]  
Cressie N., 1993, Statistics for Spatial Data, DOI [10.1002/9781119115151, DOI 10.1002/9781119115151]
[7]  
Doob JL., 1953, Stochastic Processes
[8]  
FISCHER E, 1983, INTERMEDIATE REAL AN
[9]  
Gel'fand IM., 1964, APPL HARMONIC ANAL G, V4
[10]  
GELFAND IM, 1955, DOKL AKAD NAUK SSSR+, V100, P853
123