Martingale approximations for random fields

2017/08/28 by Magda Peligrad, Na Zhang, Peligrad, Magda +1
Decision Sciences · Mathematics · #60F05 #60G10 #60G48 #60G60 #FOS: Mathematics #Mathematical Approximation and Integration #Probabilistic and Robust Engineering Design #Probability (math.PR) #Probability and Risk Models #math.PR #msc:60F05 #msc:60G10 #msc:60G48 #msc:60G60

paper · pdf · doi:10.48550/arxiv.1708.08492

11 pages

arxiv created 2017/08/28 · openalex publication_date 2017/08/28 · arxiv updated 2017/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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