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.
|Title of host publication||Random Walk, Sequential Analysis and Related Topics|
|Subtitle of host publication||A Festschrift in Honor of Yuan-Shih Chow|
|Publisher||World Scientific Publishing Co.|
|Number of pages||14|
|ISBN (Print)||9812703551, 9789812703552|
|Publication status||Published - 2006 Jan 1|
All Science Journal Classification (ASJC) codes