G. Matheron, Principles of geostatistics, Economic Geology, vol.58, issue.8, pp.1246-1266, 1963.
DOI : 10.2113/gsecongeo.58.8.1246

M. Stein, Interpolation of Spatial Data, Some Theory for Kriging, 1999.

W. J. Welch, R. J. Buck, J. Sacks, H. P. Wynn, T. J. Mitchell et al., Screening, Predicting, and Computer Experiments, Screening, predicting, and computer experiments, pp.15-25, 1992.
DOI : 10.2307/1269548

A. O. Hagan, Bayesian analysis of computer code outputs: A tutorial, Reliability Engineering & System Safety, vol.9110, issue.11, pp.1290-1300, 2006.

D. Jones, A taxonomy of global optimization methods based on response surfaces, Journal of Global Optimization, vol.21, issue.4, pp.345-383, 2001.
DOI : 10.1023/A:1012771025575

T. Santner, B. Williams, and W. Notz, The design and analysis of computer experiments, 2003.
DOI : 10.1007/978-1-4757-3799-8

A. Van-der-vaart and J. Van-zanten, Rates of contraction of posterior distributions based on Gaussian process priors, The Annals of Statistics, vol.36, issue.3, pp.1435-1463, 2008.
DOI : 10.1214/009053607000000613

A. Van-der-vaart and J. Van-zanten, Reproducing kernel Hilbert spaces of Gaussian priors, Jayanta K. Ghosh, Institute of Mathematical Statistics Collect, vol.3, pp.200-222, 2008.
DOI : 10.1214/074921708000000156

A. Van-der-vaart and H. Van-zanten, Information rates of nonparametric gaussian process methods, Journal of Machine Learning Research, vol.12, pp.2095-2119, 2011.

N. Cressie, Statistics for spatial data, Wiley series in probability and mathematical statistics, 1993.

P. Abrahamsen, A review of gaussian random fields and correlation functions, Tech. rep., Norwegian Computing Center, 1997.

H. Cramér and M. R. Leadbetter, Stationary and Related Stochastic Processes: Sample Function Properties and Their Applications, 1967.

R. J. Adler, An Introduction to Continuity, Extrema, and Related Topics for, General Gaussian Processes Lecture Notes-Monograph Series, vol.12, 1990.

M. Scheuerer, Regularity of the sample paths of a general second order random field, Stochastic Processes and their Applications, pp.1879-1897, 2010.
DOI : 10.1016/j.spa.2010.05.009

M. Scheuerer, A comparison of models and methods for spatial interpolation in statistics and numerical analysis, 2009.

K. Parthasarathy and K. Schmidt, Positive Definite Kernels, Continuous Tensor Products, and Central Limit Theorems of Probability Theory, Lecture Notes in Mathematics, vol.272, 1972.
DOI : 10.1007/BFb0058340

D. Ginsbourger, X. Bay, O. Roustant, and L. Carraro, Argumentwise invariant kernels for the approximation of invariant functions, Annales de la facult?? des sciences de Toulouse Math??matiques, vol.21, issue.3, pp.501-527, 2012.
DOI : 10.5802/afst.1343
URL : https://hal.archives-ouvertes.fr/hal-00632815

N. Durrande, D. Ginsbourger, and O. Roustant, Additive Covariance kernels for high-dimensional Gaussian Process modeling, Annales de la faculté des Sciences de Toulouse 21, pp.481-499, 2012.
DOI : 10.5802/afst.1342
URL : https://hal.archives-ouvertes.fr/hal-00644934

D. Duvenaud, H. Nickisch, and C. E. Rasmussen, Additive Gaussian processes, Advances in Neural Information Processing Systems 25, pp.1-8, 2011.

A. Berlinet and C. Thomas-agnan, Reproducing kernel Hilbert spaces in probability and statistics, 2004.
DOI : 10.1007/978-1-4419-9096-9

C. Stone, Additive regression and other nonparametric models, The Annals of, Statistics, pp.689-705, 1985.

T. Hastie and R. Tibshirani, Generalized additive models, 1990.

L. Meier, S. Van-de-geer, and P. Bühlmann, High-dimensional additive modeling, High-dimensional additive modeling, pp.3779-3821, 2009.
DOI : 10.1214/09-AOS692
URL : http://arxiv.org/abs/0806.4115

G. Raskutti, M. Wainwright, and B. Yu, Minimax-optimal rates for sparse additive models over kernel classes via convex programming, 2011.

G. Gayraud and Y. Ingster, Detection of sparse additive functions, Electron, J. Statist, vol.6, pp.1409-1448, 2012.

J. V. Liu, KarhunenLò eve expansion for additive brownian motions, Stochastic Processes and their Applications, pp.4090-4110, 2013.

R. Singh and J. Manhas, Composition Operators on Function Spaces, 1993.

T. E. Fricker, J. E. Oakley, and N. M. Urban, Multivariate Gaussian Process Emulators With Nonseparable Covariance Structures, Technometrics, vol.69, issue.1
DOI : 10.1080/00401706.2012.715835

N. Aronszajn, Theory of reproducing kernels, Transaction of the, pp.337-404, 1950.

J. Mercer, Functions of Positive and Negative Type, and their Connection with the Theory of Integral Equations, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.209, issue.441-458, pp.415-446, 1909.
DOI : 10.1098/rsta.1909.0016

H. König, Eigenvalue distribution of compact operators, 1986.
DOI : 10.1007/978-3-0348-6278-3

I. Steinwart and C. Scovel, Mercer???s Theorem on General Domains: On the Interaction between Measures, Kernels, and RKHSs, Constructive Approximation, vol.18, issue.3, pp.363-417, 2012.
DOI : 10.1007/s00365-012-9153-3

J. Kuelbs, Expansions of vectors in a Banach space related to Gaussian measures, Proceedings of the American Mathematical Society, vol.27, issue.2, pp.364-370, 1971.

T. Kadota, Differentiation of Karhunen-Loève expansion and application to optimum reception of sure signals in noise, IEEE Transactions on Information Theory, vol.13, issue.2, pp.255-260, 1967.
DOI : 10.1109/TIT.1967.1054009

P. Deheuvels, A Karhunen???Lo??ve expansion for a mean-centered Brownian bridge, Statistics & Probability Letters, vol.77, issue.12, pp.1190-1200, 2007.
DOI : 10.1016/j.spl.2007.03.011

M. Scheuerer and M. Schlather, Covariance Models for Divergence-Free and Curl-Free Random Vector Fields, Stochastic Models, vol.38, issue.3, pp.433-451, 2012.
DOI : 10.1016/j.spa.2010.05.009

R. Schaback, Solving the Laplace equation by meshless collocation using harmonic kernels, Advances in Computational Mathematics, vol.101, issue.4, pp.457-470, 2009.
DOI : 10.1007/s10444-008-9078-3

Y. Hon and R. Schaback, Solving the 3D Laplace equation by meshless collocation via harmonic kernels, Advances in Computational Mathematics, vol.31, issue.1, pp.1-19, 2013.
DOI : 10.1007/s10444-011-9224-1

I. Sobol, Theorems and examples on high dimensional model representation, Reliability Engineering & System Safety, vol.79, issue.2, pp.187-193, 2003.
DOI : 10.1016/S0951-8320(02)00229-6

F. Y. Kuo, I. H. Sloan, G. W. Wasilkowski, and H. Wozniakowski, On decompositions of multivariate functions, Mathematics of Computation, vol.79, issue.270, pp.953-966, 2010.
DOI : 10.1090/S0025-5718-09-02319-9

I. Sobol, Theorems and examples on high dimensional model representation, Reliability Engineering & System Safety, vol.79, issue.2, pp.187-193, 2003.
DOI : 10.1016/S0951-8320(02)00229-6

F. Bach, High-dimensional non-linear variable selection through hierarchical kernel learning
URL : https://hal.archives-ouvertes.fr/hal-00413473

S. Gunn and M. Brown, SUPANOVA: a sparse, transparent modelling approach, Neural Networks for Signal Processing IX: Proceedings of the 1999 IEEE Signal Processing Society Workshop (Cat. No.98TH8468), pp.21-30, 1999.
DOI : 10.1109/NNSP.1999.788119