Work

Limit theorems for weighted Bernoulli random fields under Hannan's condition

Year: 2015

Type: preprint

Abstract: Consider a Bernoulli random field satisfying the Hannan's condition. Recently, invariance principles for partial sums of random fields over rectangular index sets are established. In this note we complement previous results by investigating 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1504.01419

Authors: Klicnarová, Jana, Volný, Dalibor, Wang, Yizao

Institutions: University of South Bohemia in České Budějovice, Laboratoire de Mathématiques Raphaël Salem, Université de Rouen Normandie, University of Cincinnati

Language: English

Topic: Probability and Statistical Research

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Grantová Agentura České Republiky

Award: Martingale approximations and U-statistics

OpenAlex ID: W853392258

Cites:

Cited by: 3

Related to: 10