Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1156278 | Stochastic Processes and their Applications | 2016 | 20 Pages |
Abstract
Recently, invariance principles for partial sums of Bernoulli random fields over rectangular index sets have been proved under Hannan’s condition. In this note we complement previous results by establishing limit theorems for weighted Bernoulli random fields, including central limit theorems for partial sums over arbitrary index sets and invariance principles for Gaussian random fields. Most results improve earlier ones on Bernoulli random fields under Wu’s condition, which is stronger than Hannan’s condition.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Jana Klicnarová, Dalibor Volný, Yizao Wang,