Invariance principle via orthomartingale approximation

Davide Giraudo (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

We obtain a necessary and sufficient condition for the orthomartingale-coboundary decomposition. We establish a sufficient condition for the approximation of the partial sums of a strictly stationary random fields by those of stationary orthomartingale differences. This condition can be checked under multidimensional analogues of the Hannan condition and the Maxwell-Woodroofe condition.

Mots clés: Random fields; invariance principle; Orthomartingales; projective conditions; Maxwell and Woodroofe condition

Domaines: Probabilités [math.PR]; Systèmes dynamiques [math.DS]

Davide Giraudo. Invariance principle via orthomartingale approximation. Stochastics and Dynamics, 2018. ⟨hal-01476384v2⟩