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.

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