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

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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    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