V. V. Anh and K. E. Lunney, Parameter estimation of random fields with long-range dependence, Mathematical and Computer Modelling, vol.21, issue.9, pp.67-77, 1995.
DOI : 10.1016/0895-7177(95)00054-6

F. Avram and M. Taqqu, Noncentral Limit Theorems and Appell Polynomials, The Annals of Probability, vol.15, issue.2, pp.767-775, 1987.
DOI : 10.1214/aop/1176992170

R. F. Bass, Law of the iterated logarithm for set-indexed partial sum processes with finite variance, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.1, issue.4, pp.591-608, 1985.
DOI : 10.1007/BF00531869

A. K. Basu and C. C. Dorea, On functional central limit theorem for stationary martingale random fields, Acta Mathematica Academiae Scientiarum Hungaricae, vol.29, issue.3-4, pp.307-316, 1979.
DOI : 10.1007/BF01902565

J. Bennett and A. Khotanzad, Modeling textured images using generalized long correlation models, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.20, issue.12, pp.1365-1370, 1998.
DOI : 10.1109/34.735810

P. J. Bickel and M. J. Wichura, Convergence Criteria for Multiparameter Stochastic Processes and Some Applications, The Annals of Mathematical Statistics, vol.42, issue.5, pp.1656-1670, 1971.
DOI : 10.1214/aoms/1177693164

URL : http://projecteuclid.org/download/pdf_1/euclid.aoms/1177693164

P. Billingsley, Convergence of probability measures, 1968.
DOI : 10.1002/9780470316962

N. Bingham, C. Goldie, and J. L. Teugels, Regular variation, Encyclopedia of Mathematics and its applications, vol.27, 1987.
DOI : 10.1017/CBO9780511721434

H. Brezis, Analyse fonctionnelle : théorie et applications, 1983.

D. R. Brillinger, Time Series : Data analysis and theory, 1981.
DOI : 10.1137/1.9780898719246

P. J. Brockwell and R. A. Davis, Time Series : Theory and Methods, 1991.

A. Bulinski and M. Keane, Invariance principle for associated random fields, Journal of Mathematical Sciences, vol.40, issue.3???4, pp.2905-2911, 1996.
DOI : 10.1007/BF02362501

M. Cassandro and G. Jona-lasinio, Critical point behaviour and probability theory Advances in Physics, pp.913-941, 1978.

J. Chiles and P. Delfiner, Geostatistics : Modeling Spatial Uncertainty, 1998.
DOI : 10.1002/9781118136188

URL : https://hal.archives-ouvertes.fr/hal-00795336

N. Cressie, Statistics for spatial data, 1993.
DOI : 10.1002/9781119115151

J. Dedecker, Exponential inequalities and functional central limit theorems for random fields, ESAIM: Probability and Statistics, vol.5, pp.77-104, 2001.
DOI : 10.1051/ps:2001103

URL : http://archive.numdam.org/article/PS_2001__5__77_0.pdf

H. Dehling, T. Mikosch, and M. Sorensen, Empirical process techniques for dependent data, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00291501

H. Dehling and M. S. Taqqu, The Empirical Process of some Long-Range Dependent Sequences with an Application to $U$-Statistics, The Annals of Statistics, vol.17, issue.4, pp.1767-1783, 1989.
DOI : 10.1214/aos/1176347394

R. L. Dobrushin, Existence of a Phase Transition in Two-Dimensional and Three-Dimensional Ising Models, Theory of Probability & Its Applications, vol.10, issue.2, pp.193-213, 1965.
DOI : 10.1137/1110026

R. L. Dobrushin, Gaussian random fields -gibbsian point of view, Multicomponent random systems of Adv. in Prob. and Related Topics, 1980.

R. L. Dobrushin and P. Major, Non-central limit theorems for non-linear functional of Gaussian fields, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.31, issue.No. 1, pp.27-52, 1979.
DOI : 10.1007/BF00535673

P. Doukhan, Models, inequalities, and limit theorems for stationary sequences, Theory and applications of long-range dependence. Birkhäuser, 2003.

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

P. Doukhan and J. R. Leon, Asymptotics for the local time of a strongly dependent vector-valued Gaussian random field, Acta Mathematica Hungarica, vol.40, issue.4, pp.329-351, 1996.
DOI : 10.1007/BF02187395

P. Doukhan, J. R. Leon, and P. Soulier, Central and non central limit theorems for quadratic forms of a strongly dependent gaussian field, Brazilian Journal of Prob. and. Stat, vol.10, pp.205-223, 1996.

E. Machkouri and M. , Théorèmes limite pour les champs et les suites stationnaires de variables aléatoires réelles, 2003.

E. Machkouri, M. Volny, and D. , Contre-exemple dans le théorème limite central fonctionnel pour les champs aléatoires réels. Annales de l'Institut Henri Poincaré, pp.325-337, 2003.

K. Eom, Long-correlation image models for textures with circular and elliptical correlation structures, Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205), pp.1047-1055, 2001.
DOI : 10.1109/ICIP.2001.958987

M. E. Fisher, Correlation Functions and the Critical Region of Simple Fluids, Journal of Mathematical Physics, vol.5, issue.7, pp.944-962, 1964.
DOI : 10.1063/1.1704197

R. Fox and M. Taqqu, Central limit theorems for quadratic forms in random variables having long-range dependence, Probability Theory and Related Fields, vol.4, issue.2, pp.428-446, 1985.
DOI : 10.1007/BF00569990

R. Fox and M. Taqqu, Central limit theorem for quadratic forms in random variables having long-range dependence. Probability Theory and Related Fields, pp.213-240, 1987.

H. O. Georgii, Gibbs measure and phase transitions, 1988.

I. I. Gikhman and A. V. Skorokhod, Introduction to the theory of random processes, 1965.

L. Giraitis, P. Kokoszka, R. Leipus, and G. Teyssière, Rescaled variance and related tests for long memory in volatility and levels, Journal of Econometrics, vol.112, issue.2, pp.265-294, 2003.
DOI : 10.1016/S0304-4076(02)00197-5

L. Giraitis, R. Leipus, P. , and A. , A TEST FOR STATIONARITY VERSUS TRENDS AND UNIT ROOTS FOR A WIDE CLASS OF DEPENDENT ERRORS, Econometric Theory, vol.116, issue.06, 2002.
DOI : 10.1111/j.1467-9892.2005.00464.x

L. Giraitis and D. Surgailis, A central limit theorem for quadratic forms in strongly dependent linear variables and its application to asymptotic normality of Whittles's estimate. Probab. Theory Related Fields, pp.87-104, 1990.

C. Granger and R. Joyeux, AN INTRODUCTION TO LONG-MEMORY TIME SERIES MODELS AND FRACTIONAL DIFFERENCING, Journal of Time Series Analysis, vol.7, issue.1, pp.15-30, 1980.
DOI : 10.2307/3212527

C. W. Granger, Long memory relationships and the aggregation of dynamic models, Journal of Econometrics, vol.14, issue.2, pp.227-238, 1980.
DOI : 10.1016/0304-4076(80)90092-5

H. Gray, N. Zhang, and W. Woodward, ON GENERALIZED FRACTIONAL PROCESSES, Journal of Time Series Analysis, vol.7, issue.12, pp.233-257, 1989.
DOI : 10.2307/2287515

L. Grinblatt, A limit theorem for measurable random processes and its applications, Proc. of the American Math, pp.61371-376, 1976.
DOI : 10.1090/S0002-9939-1976-0423450-2

X. Guyon, Champs aléatoires sur un réseau, 1993.

C. C. Heyde and R. Gay, Smoothed periodogram asymptotics and estimation for processes and fields with possible long-range dependence, Stochastic Processes and their Applications, pp.169-182, 1993.
DOI : 10.1016/0304-4149(93)90067-E

URL : http://doi.org/10.1016/0304-4149(93)90067-e

J. R. Hosking, Fractional differencing, Biometrika, vol.68, issue.1, pp.165-176, 1981.
DOI : 10.1093/biomet/68.1.165

J. R. Hosking, Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series, Journal of Econometrics, vol.73, issue.1, pp.261-284, 1996.
DOI : 10.1016/0304-4076(95)01740-2

R. Kashyap and K. Eom, Texture boundary detection based on the long correlation model, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.11, issue.1, pp.58-67, 1989.
DOI : 10.1109/34.23113

R. Kashyap and P. Lapsa, Synthesis ans estimation of random fields using longcorrelation models, IEEE Trans. Pattern Anal. Machine Intell, issue.6, pp.6800-809, 1984.

B. Kaufman and L. Onsager, Crystal Statistics. III. Short-Range Order in a Binary Ising Lattice, Physical Review, vol.76, issue.8, pp.1244-1252, 1949.
DOI : 10.1103/PhysRev.76.1244

M. Kendall and A. Stuart, The advanced theory of statistics, 1958.

J. M. Kosterlitz and D. J. Thouless, Two-dimensional physics, Progess in Low Temperature Physics, p.371, 1978.

D. Kwiatoski, P. C. Phillips, P. Schmidt, and Y. Shin, Testing the null hypothesis of stationarity against the alternative of a unit root, Journal of Econometrics, vol.54, issue.1-3, pp.159-178, 1992.
DOI : 10.1016/0304-4076(92)90104-Y

H. Künsch, Reellwertige Zufallsfelder auf einem Gitter : Interpolationsprobleme, Variationsprinzip und statistische Analyse, 1980.

G. Lang and P. Soulier, Convergence de mesures spectrales aléatoires et applications à des principes d'invariance, Statistical Inference for Stochastic Processes, vol.3, issue.1/2, pp.41-51, 2000.
DOI : 10.1023/A:1009941503489

F. Lavancier, Invariance principles for non-isotropic long memory random fields. preprint, 2005.

F. Lavancier, Long memory random fields. à paraître dans un ouvrage collectif chez Springer, 2005.
URL : https://hal.archives-ouvertes.fr/tel-00012045

F. Lavancier, Processus empirique de fonctionnelles de champs gaussiens à longue memoire. preprint 63, 2005.
DOI : 10.1016/j.crma.2005.12.029

H. S. Lee and P. Schmidt, On the power of the KPSS test of stationarity against fractionally-integrated alternatives, Journal of Econometrics, vol.73, issue.1, pp.285-302, 1996.
DOI : 10.1016/0304-4076(95)01741-0

N. Leonenko, Limit Theorems for Random Fields with Singular Spectrum, 1999.
DOI : 10.1007/978-94-011-4607-4

N. Leonenko and M. Bensic, On estimation of regression coefficients of long memory random fields observed on the arrays, Random Operators and Stochastic Equations, vol.6, issue.1, pp.61-76, 1998.
DOI : 10.1515/rose.1998.6.1.61

A. Lo, Long-Term Memory in Stock Market Prices, Econometrica, vol.59, issue.5, pp.1279-1313, 1991.
DOI : 10.2307/2938368

P. Major, Multiple Wiener-Itô Integrals. Number 849 in Lecture Notes in Mathematics, 1981.

D. Marinucci and S. Poghosyan, Asymptotics for linear random fields, Statistics & Probability Letters, vol.51, issue.2, pp.131-141, 2001.
DOI : 10.1016/S0167-7152(00)00139-5

L. Onsager, Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition, Physical Review, vol.65, issue.3-4, pp.117-149, 1944.
DOI : 10.1103/PhysRev.65.117

G. Oppenheim and M. Viano, Aggregation of random parameters Ornstein-Uhlenbeck or AR processes: some convergence results, Journal of Time Series Analysis, vol.16, issue.3, pp.335-350, 2004.
DOI : 10.1016/0167-7152(94)00015-8

O. Haye and M. , Théorèmes limites pour des processus à longue mémoire saisonnière, 2001.

O. Haye and M. , Asymptotic behavior of the Empirical Process for Gaussian data presenting seasonal long-memory, ESAIM: Probability and Statistics, vol.6, pp.293-309, 2002.
DOI : 10.1051/ps:2002016

B. Pesquet-popescu and J. Pesquet, Synthesis of bidimensional alpha-stable models with long-range dependence, Signal Processing, issue.82, pp.1927-1940, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00621853

D. K. Pickard, Inference for Discrete Markov Fields: The Simplest Nontrivial Case, Journal of the American Statistical Association, vol.19, issue.397, pp.90-96, 1987.
DOI : 10.1080/01621459.1987.10478394

D. Pollard, Convergence of stochastic processes, 1984.
DOI : 10.1007/978-1-4612-5254-2

M. Rosenblatt, Stationary sequences and random fields, 1985.
DOI : 10.1007/978-1-4612-5156-9

S. Sethuraman and I. V. Basawa, Maximum likelihood estimation for a fractionally differenced autoregressive model on a two-dimensional lattice, Journal of Statistical Planning and Inference, vol.44, issue.2, pp.219-235, 1995.
DOI : 10.1016/0378-3758(94)00046-X

D. Surgailis, Zones of attraction of self-similar multiple integrals, Lithuanian Mathematical Journal, vol.50, issue.No. 1, pp.327-340, 1982.
DOI : 10.1007/BF00966427

M. Taqqu, Convergence of integrated processes of arbitrary Hermite rank, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.7, issue.1, pp.53-83, 1979.
DOI : 10.1007/BF00535674

N. Terrin and M. Taqqu, A noncentral limit theorem for quadratic forms of Gaussian stationary sequences, Journal of Theoretical Probability, vol.31, issue.3, pp.449-475, 1990.
DOI : 10.1007/BF01061262

T. Van-der-meer, Invariance principle for strongly dependent sequences, Prépub. Lab. Prob. et Stat, 1996.

M. Viano, C. Deniau, and G. Oppenheim, LONG-RANGE DEPENDENCE AND MIXING FOR DISCRETE TIME FRACTIONAL PROCESSES, Journal of Time Series Analysis, vol.6, issue.2, pp.323-338, 1995.
DOI : 10.1111/j.1467-9892.1995.tb00237.x

S. Wainger, Special trigonometric series in k-dimensions. Number 59, 1965.

M. Wichura, Inequalities with Applications to the Weak Convergence of Random Processes with Multi-Dimensional Time Parameters, The Annals of Mathematical Statistics, vol.40, issue.2, pp.681-687, 1969.
DOI : 10.1214/aoms/1177697741

A. Zygmund, Trigonometric series, 1959.