Le théorème limite centrale pour un champ aléatoire f◦ Ti, i∈ Zd, de différences d'une
martingale est démontré. Le résultat est connu pour les champs aléatoires de Bernoulli; ici …

We obtain a necessary and sufficient condition for the orthomartingale-coboundary
decomposition. We establish a sufficient condition for the approximation of the partial sums …

Motivated by random evolutions which do not start from equilibrium, in a recent work,
Peligrad and Volný (J Theor Probab, 2018. arxiv: 1802.09106) showed that the central limit …

In this paper we provide necessary and sufficient conditions for the mean square
approximation of a random field by an ortho-martingale. The conditions are formulated in …

Let\mathcal SS be an abelian group of automorphisms of a probability space (X,\mathcal A,
μ)(X, A, μ) with a finite system of generators (A_1, ..., A_d).(A 1,…, A d). Let A^ ℓ A ℓ ̲ denote …

We provide a new projective condition for a stationary real random field indexed by the
lattice ℤ d to be well approximated by an orthomartingale in the sense of Cairoli (1969). Our …

We prove a central limit theorem for strictly stationary random fields under a sharp projective
condition. The assumption was introduced in the setting of random sequences by Maxwell …

We consider a field f∘ T 1 i 1∘…∘ T did ∘ T _1^ i_1 ∘\dots ∘ T _d^ i_d, where T 1,..., T d are
completely commuting transformations in the sense of Gordin. If one of these transformations …

In this paper, we study the central limit theorem and its functional form for random fields
which are started not from their equilibrium, but rather under the measure conditioned by the …

Recently, invariance principles for partial sums of Bernoulli random fields over rectangular
index sets have been proved under Hannan's condition. In this note we complement …