S. Abramowitz, M. Abramowitz, and I. A. Stegun, Handbook of Mathematical Functions, American Journal of Physics, vol.34, issue.2, 1965.
DOI : 10.1119/1.1972842

. Berger, Objective Bayesian Analysis of Spatially Correlated Data, Journal of the American Statistical Association, vol.96, issue.456, pp.1361-1374, 2001.
DOI : 10.1198/016214501753382282

J. C. Bronski, Asymptotics of Karhunen-Loeve Eigenvalues and Tight Constants for Probability Distributions of Passive Scalar Transport, Communications in Mathematical Physics, vol.238, issue.3, pp.563-582, 2003.
DOI : 10.1007/s00220-003-0835-3

. Fernex, The Moret 4b monte carlo code new features to treat complex criticality systems, MandC International Conference on Mathematics and Computation Supercomputing, Reactor and Nuclear and Biological Application, 2005.

. Gneiting, Mat??rn Cross-Covariance Functions for Multivariate Random Fields, Journal of the American Statistical Association, vol.105, issue.491, pp.1167-1177, 2010.
DOI : 10.1198/jasa.2010.tm09420

D. A. Harville, Matrix Algebra from Statistician's Perspective, 1997.

G. M. Laslett, Kriging and Splines: An Empirical Comparison of their Predictive Performance in Some Applications, Journal of the American Statistical Association, vol.44, issue.426, pp.391-400, 1994.
DOI : 10.1007/BF00893314

J. Mercer, Functions of positive and negative type and their connection with the theory of integral equations, Philosophical Transactions of the Royal Society A, vol.209, pp.441-458, 1909.

[. Zuniga, Adaptive directional stratification for controlled estimation of the probability of a rare event, Reliability Engineering & System Safety, vol.96, issue.12, pp.1691-1712, 2011.
DOI : 10.1016/j.ress.2011.06.016

A. I. Nazarov and Y. Y. Nikitin, Exact l 2 small ball behaviour of integrated Gaussian processes and spectral asymptotics of boundary value problems, pp.469-494, 2004.

V. Opper, M. Opper, and F. Vivarelli, General bounds on Bayes errors for regression with Gaussian processes, Advances in Neural Information Processing Systems 11, pp.302-308, 1999.

V. Picheny, Improving Accuracy and Compensating for Uncertainty in Surrogate Modeling, 2009.
URL : https://hal.archives-ouvertes.fr/tel-00770844

R. S. Pusev, Small Deviations Asymptotics for Mat??rn Processes and Fields under Weighted Quadratic Norm, Theory of Probability & Its Applications, vol.55, issue.1, pp.164-172, 2011.
DOI : 10.1137/S0040585X97984723

W. Rasmussen, C. E. Rasmussen, and C. K. Williams, Gaussian Processes in Machine Learning, 2006.
DOI : 10.1162/089976602317250933

URL : http://hdl.handle.net/11858/00-001M-0000-0013-F365-A

K. Ritter, Almost Optimal Differentiation Using Noisy Data, Journal of Approximation Theory, vol.86, issue.3, pp.293-309, 2000.
DOI : 10.1006/jath.1996.0071

URL : http://doi.org/10.1006/jath.1996.0071

K. Ritter, Average-Case Analysis of Numerical Problems, 2000.
DOI : 10.1007/BFb0103934

. Sacks, Design and Analysis of Computer Experiments, Statistical Science, vol.4, issue.4, pp.409-423, 1989.
DOI : 10.1214/ss/1177012413

J. Sacks and D. Ylvisaker, Variance estimation for approximately linear models, Series Statistics, vol.6, issue.2, pp.147-162, 1981.
DOI : 10.1080/02331888108801577

D. F. Shanno, Conditioning of quasi-Newton methods for function minimization, Mathematics of Computation, vol.24, issue.111, pp.647-656, 1970.
DOI : 10.1090/S0025-5718-1970-0274029-X

H. Sollich, P. Sollich, and A. Halees, Learning Curves for Gaussian Process Regression: Approximations and Bounds, Neural Computation, vol.47, issue.1, pp.1393-1428, 2002.
DOI : 10.1023/A:1007601601278

URL : http://arxiv.org/abs/cond-mat/0105015

M. L. Stein, Interpolation of Spatial Data, 1999.
DOI : 10.1007/978-1-4612-1494-6

R. A. Todor, Robust Eigenvalue Computation for Smoothing Operators, SIAM Journal on Numerical Analysis, vol.44, issue.2, pp.865-878, 2006.
DOI : 10.1137/040616449

H. Wackernagel, Multivariate Geostatistics, 2003.

V. Williams, C. K. Williams, and F. Vivarelli, Upper and lower bounds on the learning curve for Gaussian processes, Machine Learning, pp.77-102, 2000.