ON THE PREDICTION-THEORY OF 2-PARAMETER STATIONARY RANDOM-FIELDS

被引：17

作者：

KALLIANPUR, G

MIAMEE, AG

NIEMI, H

机构：

[1] HAMPTON UNIV, HAMPTON, VA USA

[2] UNIV HELSINKI, SF-00100 HELSINKI 10, FINLAND

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 1990年 / 32卷 / 01期

关键词：

concordance; deterministic spectral decomposition; innovation; minimality; multiplicity; purely nondeterministic; second-order stationary random fields; Wold decomposition;

D O I：

10.1016/0047-259X(90)90076-T

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：

The paper develops the spectral theory corresponding to the various time domain Wold decompositions of a discrete two-parameter stationary second-order random field (ssorf). Appropriate Szegö-type error formulas are established. Minimality and interpolability are defined for ssorf's and sufficient spectral criteria for these are derived. Partial results are also obtained which help to determine, via spectral methods, some of the multiplicities introduced by Kallianpur and Mandrekar in their time domain analysis of ssorf's. © 1990.

引用

页码：120 / 149

页数：30

共 13 条

[1] [Anonymous], 1985, STATIONARY SEQUENCES
[2] CHIANG TP, 1957, THEOR PROBAB APPL, V2, P58
[3] Grenander U., 1958, TOEPLITZ FORMS THEIR
[4] PREDICTION THEORY AND FOURIER SERIES IN SEVERAL VARIABLES
HELSON, H
LOWDENSLAGER, D
[J]. ACTA MATHEMATICA, 1958, 99 (3-4) : 165 - 202
[5] HELSON H, 1961, ACTA MATH, V106, P173
[6] KALLIANPUR G, 1987, 178 U N CAR CTR STOC
[7] Kallianpur G., 1983, PREDICTION THEORY HA, P165
[8] KOREZLIOGLU H, 1987, 6TH P FRANC BELG M S
[9] THE PREDICTION THEORY OF MULTIVARIATE STOCHASTIC PROCESSES .3. UNBOUNDED SPECTRAL DENSITIES
MASANI, P
[J]. ACTA MATHEMATICA, 1960, 104 (1-2) : 141 - 162
[10] MASANI P, 1966, MULTIVARIATE ANAL, V1, P351

← 1 2 →