Invariance principles for non-isotropic long memory random fields

Billingsley P (1968) Convergence of probability measures. Wiley, New York

Breuer P, Major P (1983) Central limit theorems for non-linear functionals of gaussian fields. J Mulivar Analy 13:425–441

Dobrushin RL, Major P (1979) Non central limit theorems for non-linear functionals of gaussian fields. Z Warsch verw Geb 50:27–52

Doukhan P, Lang G, Surgailis D (2002) Asymptotics of weighted empirical processes of linear fields with long-rang dependence. Ann Inst Henri Poincaré 6:879–896

Gikhman II, Skorokhod AV (1965) Introduction to the theory of random processes. W. B. Saunders, Philadelphia

Grinblatt L (1976) A limit theorem for measurable random processes and its applications. Proc Am Math Soc 61(2):371–376

Lang G, Soulier P (2000) Convergence de mesures spectrales aléatoires et applications à des principes d’invariance. Stat Inf Stoch Proc 3:41–51

Lavancier F (2003a) Principes d’invariance pour les champs aléatoires fortement dépendants, partie 1: théorème de convergence de champs spectraux. Technical Report 60, XII, IRMA, Lille. availaible at http://math.univ-lille1.fr/lavancier

Lavancier F (2003b) Principes d’invariance pour les champs aléatoires fortement dépendants, partie 2: application aux sommes partielles de champs aléatoires à longe mémoire. Technical Report 61, V, IRMA, Lille. availaible at http://math.univ-lille1.fr/lavancier

Viano M-C, Deniau C, Oppenheim G (1995) Long-range dependence and mixing for discrete time fractional processes. J Time Ser Anal 16(3):323–338

Wainger S (1965) Special trigonometric series in k-dimensions. Number 59. AMS, Providence. RI