On spectral and random measures associated to discrete and continuous-time processes
type: Item
instance of: scholarly article
title: On spectral and random measures associated to discrete and continuous-time processes
zbMATH Open document ID: 1019.60004
DOI: 10.1016/S0167-7152(02)00142-6
author: Alain Boudou
author: Y. Romain
published in: Statistics \& Probability Letters
publication date: 2003-05-07T00:00:00Z
review text: For each \(i=1, 2\), let \((X_{g_i})_{g_i\in G_i}\) be a complex Hilbertian stationary process where the index space \(G_i\) is a locally compact Abelian group with dual space admitting a countable basis. Let \(Z_i\) (respectively \(\varepsilon_i\)) denote a random measure (respectively spectral measure) associated to the stationary process \((X_{g_i})_{g_i\in G_i}\), \(i=1, 2.\) Tensor products \(\varepsilon_1\otimes \varepsilon_2\) and \(Z_1\otimes Z_2\) are studied for both continuous and discrete time spaces. An example for the product of scalar and vector-valued stationary processes is given.
Mathematics Subject Classification ID: 60B11
Mathematics Subject Classification ID: 28B05
zbMATH DE Number: 1906950
zbMATH Keywords: random measure
zbMATH Keywords: spectral measure
zbMATH Keywords: tensor product
zbMATH Keywords: product of measures
zbMATH Keywords: convolution measure
zbMATH Keywords: stationary process
zbMATH Keywords: Fubini type theorem
MaRDI profile type: Publication
cites work: Q3336540
cites work: Tensor product of a finite number of spectral measures is always a spectral measure
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cites work: Q4082810
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cites work: Tensor products and statistics
cites work: Perturbation of functional tensors with applications to covariance operators.
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description: scientific article; zbMATH DE number 1906950