On the weak invariance principle for ortho-martingale in Banach spaces. Application to stationary random fields

Han-Mai Lin and Florence Merlevède

Stochastic Processes and their Applications, 2022, vol. 153, issue C, 198-220

Abstract: In this paper, we study the weak invariance principle for stationary ortho-martingales with values in 2-smooth or cotype 2 Banach spaces. Then, with the help of a suitable maximal ortho-martingale approximation, we derive the weak invariance principle for stationary random fields in Lp, 1≤p≤2, under a condition in the spirit of Hannan. As an application, we get an asymptotic result for the Lp-distances (1≤p≤2) between the common distribution function and the corresponding empirical distribution function of stationary random fields.

Keywords: Invariance principle; Random field; Ortho-martingale approximation; Empirical distribution function; Lp-distances; Wasserstein distance (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2022.08.003

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