Hölderian invariance principle for martingale difference random fields

Davide Giraudo (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

We investigate the convergence in Hölder spaces of the summation process based on the collection of products of d intervals and associated to a strictly stationary orthomartingale random field. We give a sufficient condition in terms of the law of the common distribution and the conditional variances, and we discuss its sharpness. The main tools of the proof are a tightness criterion in Hölder spaces for the multidimensional summa-tion processes associated to a strictly stationary random field and a probability inequality for strictly stationary orthomartingale random fields. Finally, we obtain by approximation a Hannan type condition.

Mots clés: Random Fields; Orthomartingales; Invariance principle; Hölder spaces

Domaines: Probabilités [math.PR]

Davide Giraudo. Hölderian invariance principle for martingale difference random fields. 2016. ⟨hal-01280885v1⟩