Electronic Communications in Probability

Martingale approximations for random fields

Peligrad Magda and Na Zhang

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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

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

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

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Zentralblatt MATH identifier

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

random field martingale approximation central limit theorem

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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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