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Pré-Publication, Document De Travail Année : 2022

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

Résumé

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 L 1 under a condition in the spirit of Hannan. As an application, we get an asymptotic result for the L 1-Wasserstein distance between the common distribution function and the corresponding empirical distribution function of stationary random fields.
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Dates et versions

hal-03603363 , version 1 (09-03-2022)

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  • HAL Id : hal-03603363 , version 1

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Han-Mai Lin, Florence Merlevède. On the weak invariance principle for ortho-martingale in Banach spaces. Application to stationary random fields. 2022. ⟨hal-03603363⟩
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