Invariance principle via orthomartingale approximation

Abstract

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.

References in corpus (8)

• Martingale approximations for sums of stationary processes
• A new maximal inequality and invariance principle for stationary sequences
• On martingale approximations
• Law of the iterated logarithm for stationary processes
• Comparison between criteria leading to the weak invariance principle
• A quenched invariance principle for stationary processes
• Independence of Four Projective Criteria for the Weak Invariance Principle
• Orthomartingale-coboundary decomposition for stationary random fields

Cited by in corpus (4)

• Bound on the maximal function associated to the bounded law of the iterated logarithms via orthomartingale approximation
• Martingale approximations for random fields
• Central limit theorem for Fourier transform and periodogram of random fields
• An exponential inequality for orthomartingale differences random fields and some applications