Electronic Communications in Probability

Martingale approximations for random fields

Peligrad Magda and Na Zhang

Full-text: Open access

Abstract

In this paper we provide necessary and sufficient conditions for the mean square approximation of a random field by an ortho-martingale. The conditions are formulated in terms of projective criteria. Applications are given to linear and nonlinear random fields with independent innovations.

Article information

Source
Electron. Commun. Probab., Volume 23 (2018), paper no. 28, 9 pp.

Dates
Received: 29 August 2017
Accepted: 3 April 2018
First available in Project Euclid: 28 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1524881136

Digital Object Identifier
doi:10.1214/18-ECP128

Mathematical Reviews number (MathSciNet)
MR3798239

Zentralblatt MATH identifier
1390.60186

Subjects
Primary: 60G60: Random fields 60G48: Generalizations of martingales 60F05: Central limit and other weak theorems 60G10: Stationary processes

Keywords
random field martingale approximation central limit theorem

Rights
Creative Commons Attribution 4.0 International License.

Citation

Magda, Peligrad; Zhang, Na. Martingale approximations for random fields. Electron. Commun. Probab. 23 (2018), paper no. 28, 9 pp. doi:10.1214/18-ECP128. https://projecteuclid.org/euclid.ecp/1524881136


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