P. Ailliot, A. Baxevani, A. Cuzol, V. Monbet, and N. Raillard, Space-time models for moving fields with an application to significant wave height fields, Environmetrics, vol.22, issue.3, pp.354-369, 2011.

J. Angulo, M. Ruiz-medina, and V. Anh, Estimation and filtering of fractional generalised random fields, Journal of the Australian Mathematical Society, vol.69, issue.3, pp.336-361, 2000.

V. Anh, J. Angulo, and M. Ruiz-medina, Possible long-range dependence in fractional random fields, Journal of Statistical Planning and Inference, vol.80, issue.1-2, pp.95-110, 1999.

S. Armstrong, T. Kuusi, and J. Mourrat, Quantitative stochastic homogenization and large-scale regularity, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01728747

A. Barth and A. Lang, Simulation of stochastic partial differential equations using finite element methods, Stochastics An International Journal of Probability and Stochastic Processes, vol.84, issue.2-3, pp.217-231, 2012.

D. Bolin and K. Kirchner, The SPDE approach for Gaussian random fields with general smoothness, 2017.

D. Bolin and F. Lindgren, Spatial models generated by nested stochastic partial differential equations, with an application to global ozone mapping, The Annals of Applied Statistics, vol.5, issue.1, pp.523-550, 2011.

N. Bourbaki, , 1965.

D. Braess, Finite elements: Theory, fast solvers, and applications in solid mechanics, 2007.

C. Bréhier, M. Hairer, and A. M. Stuart, Weak error estimates for trajectories of SPDEs for Spectral Galerkin discretization, 2016.

M. Cameletti, F. Lindgren, D. Simpson, and H. Rue, Spatio-temporal modeling of particulate matter concentration through the SPDE approach, AStA Advances in Statistical Analysis, vol.97, issue.2, pp.109-131, 2013.

C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods, p.285, 2006.
URL : https://hal.archives-ouvertes.fr/hal-01296839

P. Cartier, Processus aléatoires généralisés. Séminaire Bourbaki, vol.8, pp.425-434, 1963.

J. Chilès and P. Delfiner, Geostatistics: Modeling Spatial Uncertainty, 1999.

F. Clément and V. Martin, The Lax-Milgram Theorem. A detailed proof to be formalized in Coq, 2016.

J. W. Cooley and J. W. Tukey, An algorithm for the machine calculation of complex Fourier series, Mathematics of computation, vol.19, issue.90, pp.297-301, 1965.

F. Dai and Y. Xu, Approximation theory and harmonic analysis on spheres and balls, 2013.

S. De-iaco, D. E. Myers, and D. Posa, Space-time analysis using a general product-sum model, Statistics & Probability Letters, vol.52, issue.1, pp.21-28, 2001.

A. Deitmar, A First Course in Harmonic Analysis, 2005.

C. Dellacherie and P. Meyer, Probabilities and Potential, 1978.

F. Demengel and G. Demengel, Mesures et Distributions. Théorie et illustration par les exemples. Ellipses, 2000.

P. Dierolf and J. Voigt, Convolution and S I -Convolution of Distributions, Collectanea Mathematica, vol.29, issue.3, pp.185-196, 1978.

A. Dong, Estimation géostatistique des phénomènes régis par des équations aux dérivées partielles (Unpublished doctoral dissertation), 1990.

W. F. Donoghue, Distributions and Fourier Transform, 1969.

J. L. Doob, Stochastic processes, vol.7, 1953.

N. Dunford and J. T. Schwartz, Linear operators part I: general theory, Interscience publishers, vol.7, 1958.

X. Emery, D. Arroyo, and E. Porcu, An improved spectral turning-bands algorithm for simulating stationary vector Gaussian random fields. Stochastic environmental research and risk assessment, vol.30, pp.1863-1873, 2016.

F. Fouedjio, Contributions à la modélisation et à l'inférence des fonctions aléatoires non-stationnaires de second ordr, 2014.

G. Fuglstad, D. Simpson, F. Lindgren, and H. Rue, Non-stationary spatial modelling with applications to spatial prediction of precipitation, 2013.

E. Gabriel, Estimating second-order characteristics of inhomogeneous spatio-temporal point processes, Methodology and Computing in Applied Probability, vol.16, issue.2, pp.411-431, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00818145

E. Gabriel, J. Coville, and J. Chadoeuf, Estimating the intensity function of spatial point processes outside the observation window, Spatial Statistics, vol.22, pp.225-239, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01607360

R. Gay and C. Heyde, On a class of random field models which allows long range dependence, Biometrika, pp.401-403, 1990.

I. M. Gelfand, Generalized random processes, Dokl. Akad. Nauk SSSR(N.S, issue.100, pp.853-856, 1955.

I. M. Gelfand and N. I. Vilenkin, applications of harmonic analysis, Generalized functions, vol.4, 1964.

T. Gneiting, Nonseparable, stationary covariance functions for space-time data, Journal of the American Statistical Association, vol.97, issue.458, pp.590-600, 2002.

T. Gneiting, M. G. Genton, and P. Guttorp, Geostatistical space-time models, stationarity, separability, and full symmetry, Monographs On Statistics and Applied Probability, vol.107, p.151, 2006.

D. Gottlieb and S. A. Orszag, Numerical analysis of spectral methods: theory and applications, vol.26, 1977.

I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, 2014.

A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, vol.16, 1955.

E. D. Habil, Double sequences and double series, IUG Journal of Natural Studies, vol.14, issue.1, 2016.

M. Hairer, Solving the KPZ equation, Annals of Mathematics, pp.559-664, 2013.

M. Hairer, A theory of regularity structures. Inventiones mathematicae, vol.198, pp.269-504, 2014.

V. Heine, Models for two-dimensional stationary stochastic processes, Biometrika, vol.42, issue.1-2, pp.170-178, 1955.

H. Holden, B. Øksendal, J. Ubøe, and T. Zhang, , 2009.

, Stochastic Partial Differential Equations: a modeling, White Noise functional approach

J. Horowitz, Une remarque sur les bimesures. Séminaire de probabilités de Strasbourg, vol.11, pp.59-64, 1977.

J. Horowitz, Gaussian random measures. Stochastic processes and their applications, vol.22, pp.129-133, 1986.

D. T. Hristopulos and I. C. Tsantili, Space-time models based on random fields with local interactions, International Journal of Modern Physics B, vol.30, issue.15, p.1541007, 2016.

J. Huang, B. P. Malone, B. Minasny, A. B. Mcbratney, and J. Triantafilis, Evaluating a Bayesian modelling approach (INLA-SPDE) for environmental mapping, Science of the Total Environment, vol.609, pp.621-632, 2017.

K. Itô, Stationary random distributions. Memoirs of the College of Science, University of Kyoto. Series A: Mathematics, vol.28, issue.3, pp.209-223, 1954.

R. H. Jones, Fitting a stochastic partial differential equation to aquifer data, Stochastic Hydrology and Hydraulics, vol.3, issue.2, pp.85-96, 1989.

R. H. Jones and Y. Zhang, Models for continuous stationary space-time processes, Modelling longitudinal and spatially correlated data, pp.289-298, 1997.

E. B. Kaergaard, Spectral methods for uncertainty quantification (Unpublished master's thesis), 2013.

O. Kallenberg, Random measures, theory and applications, 2017.

M. Kardar, G. Parisi, and Y. Zhang, Dynamic scaling of growing interfaces, Physical Review Letters, vol.56, issue.9, p.889, 1986.

M. Y. Kelbert, N. N. Leonenko, and M. Ruiz-medina, Fractional random fields associated with stochastic fractional heat equations, Advances in Applied Probability, vol.37, issue.1, pp.108-133, 2005.

A. Khintchine, Korrelationstheorie der stationären stochastischen Prozesse, Mathematische Annalen, vol.109, issue.1, pp.604-615, 1934.

J. Kingman, Completely random measures, Pacific Journal of Mathematics, vol.21, issue.1, pp.59-78, 1967.

A. W. Knapp, Basic real analysis: along with companion volume Advanced real analysis, 2005.

A. N. Kolmogorov, Foundations of the Theory of Probability: Second English Edition, 1956.

A. N. Kolmogorov and Y. V. Prokhorov, Random Functions and Limit Theorems, Probability theory and mathematical statistics (chap. 44), vol.2, 1992.

J. Kupka, The Carathéodory extension theorem for vector valued measures, Proceedings of the, vol.72, pp.57-61, 1978.

A. Lang, Simulation of stochastic partial differential equations and stochastic active contours (Unpublished doctoral dissertation), 2007.

A. Lang and J. Potthoff, Fast simulation of Gaussian random fields, Monte Carlo Methods and Applications, vol.17, issue.3, pp.195-214, 2011.

A. Lang and C. Schwab, Isotropic Gaussian random fields on the sphere: Regularity, fast simulation and stochastic partial differential equations, The Annals of Applied Probability, vol.25, issue.6, pp.3047-3094, 2015.

C. Lantuéjoul, Geostatistical Simulation: Models and Algorithms, 2013.

S. Lim and L. Teo, Generalized Whittle-Matérn random field as a model of correlated fluctuations, Journal of Physics A: Mathematical and Theoretical, vol.42, issue.10, p.105202, 2009.

F. Lindgren, H. Rue, and J. Lindström, An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.73, issue.4, pp.423-498, 2011.

X. Liu, S. Guillas, and M. Lai, Efficient spatial modeling using the SPDE approach with bivariate splines, Journal of Computational and Graphical Statistics, vol.25, issue.4, pp.1176-1194, 2016.

M. Loève, Graduate texts in mathematics, Probability theory, vol.II, pp.0-387, 1978.

C. Ma, Construction of non-Gaussian random fields with any given correlation structure, Journal of Statistical Planning and Inference, vol.139, issue.3, pp.780-787, 2009.

F. Mainardi, Y. Luchko, and G. Pagnini, The fundamental solution of the space-time fractional diffusion equation, 2007.

G. Matheron, Les variables régionalisées et leur estimation: une application de la théorie des fonctions aléatoires aux Masson et CIE, 1965.

H. Mena and L. Pfurtscheller, An efficient SPDE approach for El Niz?no, 2017.

B. Minasny and A. B. Mcbratney, The Matérn function as a general model for soil variograms, Geoderma, vol.128, issue.3-4, pp.192-207, 2005.

P. Morando, Mesures aléatoires. Séminaire de probabilités de Strasbourg, vol.3, pp.190-229, 1969.

M. Morse, Bimeasures and their integral extensions, vol.39, pp.345-356, 1955.

J. Neveu, Bases mathématiques du calcul des probabilités, 1970.

B. Øksendal, Stochastic differential equations: an introduction with applications, 2003.

E. Pardo-iguzquiza and M. Chica-olmo, The Fourier integral method: an efficient spectral method for simulation of random fields, Mathematical Geology, vol.25, issue.2, pp.177-217, 1993.

M. Pereira and N. Desassis, Efficient simulation of Gaussian Markov random fields by Chebyshev polynomial approximation, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02075386

E. Porcu, M. Bevilacqua, and M. G. Genton, Spatio-temporal covariance and cross-covariance functions of the great circle distance on a sphere, Journal of the American Statistical Association, vol.111, issue.514, pp.888-898, 2016.

M. Rao, Random and Vector Measures, 2012.

M. Reed and B. Simon, Methods of modern mathematical analysis: Functional Analysis, 1980.

I. Richards and H. K. Youn, The theory of distributions: a nontechnical introduction, 1995.

I. Richards and H. K. Youn, Localization and multiplication of distributions, Journal of the Korean Mathematical Society, vol.37, issue.3, pp.371-389, 2000.

C. Rogers, Hausdorff Measures, 1970.

L. Rogers and D. Williams, Diffusions, Markov Processes and Martingales, vol.1, 2000.

J. A. Rozanov, Markov random fields and Stochastic Partial Differential Equations. Mathematics of the USSR-Sbornik, vol.32, p.515, 1977.

Y. A. Rozanov, Markov Random Fields, 1982.

W. Rudin, Real and complex Analysis, 1987.

M. Ruiz-medina, J. Angulo, and V. Anh, Fractional generalized random fields on bounded domains, 2003.

M. D. Ruiz-medina, J. M. Angulo, G. Christakos, and R. Fernández-pascual, New compactly supported spatiotemporal covariance functions from SPDEs, Statistical Methods & Applications, vol.25, issue.1, pp.125-141, 2016.

L. Schwartz, Sur l'impossibilité de la multiplication des distributions, Comptes Rendus Hebdomadaires des Séances de L'Academie des Sciences, vol.239, issue.15, pp.847-848, 1954.

L. Schwartz, Théorie des Distributions, 1966.

R. Shiraishi and M. Itano, On the Multiplicative Products of Distributions, Journal of Science of the Hiroshima University, Series AI (Mathematics), vol.28, issue.2, pp.223-235, 1964.

F. Sigrist, H. R. Künsch, and W. A. Stahel, Stochastic partial differential equation based modelling of large space-time data sets, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.77, issue.1, pp.3-33, 2015.

D. Simpson, F. Lindgren, and H. Rue, In order to make spatial statistics computationally feasible, we need to forget about the covariance function, Environmetrics, vol.23, issue.1, pp.65-74, 2012.

K. Sobczyk, Stochastic Differential Equations: With Applications to Physics and Engineering, 1991.

G. Stefanou, The stochastic finite element method: past, present and future, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.9, pp.1031-1051, 2009.

M. L. Stein, Interpolation of spatial data: some theory for kriging, 1999.

M. L. Stein, Space-time covariance functions, Journal of the American Statistical Association, vol.100, issue.469, pp.310-321, 2005.

J. Swanson, Elementary properties of functions with one-sided limits, 2011.

M. Takahashi, On topological-additive-group-valued measures, Proceedings of the Japan Academy, vol.42, issue.4, pp.330-334, 1966.

S. A. Teukolsky, B. P. Flannery, W. Press, and W. Vetterling, Numerical recipes in C. SMR, p.693, 1992.

F. Trèves, Topological Vector Spaces, Distributions and Kernels, 1967.

A. Vecchia, A general class of models for stationary two-dimensional random processes, Biometrika, vol.72, issue.2, pp.281-291, 1985.

H. Wackernagel, Multivariate Geostatistics: an introduction with applications, 2003.

P. White and E. Porcu, Towards a Complete Picture of Covariance Functions on Spheres Cross Time, 2018.

P. Whittle, On stationary processes in the plane, Biometrika, pp.434-449, 1954.

P. Whittle, Stochastic processes in several dimensions, Bulletin of the International Statistical Institute, vol.40, issue.2, pp.974-994, 1963.

D. Williams, Probability with Martingales, 1990.

A. M. Yaglom, Correlation theory of stationary and related random functions I: Basic Results, 1987.

T. Zhang and H. Zhang, Non-Fully Symmetric Space-Time Matérn Covariance Functions

O. C. Zienkiewicz, R. L. Taylor, and J. Z. Zhu, The Finite Element Method: Its Basis and Fundamentals: Its Basis and Fundamentals, 2013.