Central limit theorems for instantaneous filters of linear random fields on Z2

Tsung-Lin Cheng, Hwai Chung Ho

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Citations (Scopus)

Abstract

This note considers the stationary sequence generated by applying an instantaneous filter to a linear random field in Z2. The class of filters under consideration includes polynomials and indicator functions. Instead of imposing certain mixing conditions on the random fields, it is assumed that the weights of the innovations satisfy a summability property. By building a martingale decomposition based on a suitable filtration, asymptotic normality is proved for the partial sums of the stationary sequence.

Original languageEnglish
Title of host publicationRandom Walk, Sequential Analysis and Related Topics
Subtitle of host publicationA Festschrift in Honor of Yuan-Shih Chow
PublisherWorld Scientific Publishing Co.
Pages71-84
Number of pages14
ISBN (Electronic)9789812772558
ISBN (Print)9812703551, 9789812703552
DOIs
Publication statusPublished - 2006 Jan 1

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Stationary Sequences
Central limit theorem
Random Field
Instantaneous
Filter
Indicator function
Mixing Conditions
Summability
Partial Sums
Polynomial function
Asymptotic Normality
Martingale
Filtration
Decompose
Innovation
Class

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Cheng, T-L., & Ho, H. C. (2006). Central limit theorems for instantaneous filters of linear random fields on Z2 In Random Walk, Sequential Analysis and Related Topics: A Festschrift in Honor of Yuan-Shih Chow (pp. 71-84). World Scientific Publishing Co.. https://doi.org/10.1142/9789812772558_0005
Cheng, Tsung-Lin ; Ho, Hwai Chung. / Central limit theorems for instantaneous filters of linear random fields on Z2 Random Walk, Sequential Analysis and Related Topics: A Festschrift in Honor of Yuan-Shih Chow. World Scientific Publishing Co., 2006. pp. 71-84
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Cheng, T-L & Ho, HC 2006, Central limit theorems for instantaneous filters of linear random fields on Z2 in Random Walk, Sequential Analysis and Related Topics: A Festschrift in Honor of Yuan-Shih Chow. World Scientific Publishing Co., pp. 71-84. https://doi.org/10.1142/9789812772558_0005

Central limit theorems for instantaneous filters of linear random fields on Z2 . / Cheng, Tsung-Lin; Ho, Hwai Chung.

Random Walk, Sequential Analysis and Related Topics: A Festschrift in Honor of Yuan-Shih Chow. World Scientific Publishing Co., 2006. p. 71-84.

Research output: Chapter in Book/Report/Conference proceedingChapter

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Cheng T-L, Ho HC. Central limit theorems for instantaneous filters of linear random fields on Z2 In Random Walk, Sequential Analysis and Related Topics: A Festschrift in Honor of Yuan-Shih Chow. World Scientific Publishing Co. 2006. p. 71-84 https://doi.org/10.1142/9789812772558_0005