J. Dominguez, Boundary elements in dynamics, 1993.

D. Givoli, Numerical Methods for Problems in Infinite Domains, Studies in Applied Mechanics, 1992.

I. Harari, A unified variational approach to domain-based computation of exterior problems of time-harmonic acoustics, Applied Numerical Mathematics, vol.27, issue.4, pp.417-441, 1998.
DOI : 10.1016/S0168-9274(98)00023-3

S. V. Tsynkov, Numerical solution of problems on unbounded domains. A review, Applied Numerical Mathematics, vol.27, issue.4, pp.465-532, 1998.
DOI : 10.1016/S0168-9274(98)00025-7

J. P. Wolf, Foundation vibration analysis using simple physical models, N. J, 1994.

J. Favre, Errors in geotechnics and their impact on safety, Computers & Structures, vol.67, issue.1-3, pp.37-45, 1998.
DOI : 10.1016/S0045-7949(97)00154-5

G. I. Schuëller, A state-of-the-art report on computational stochastic mechanics, Probabilistic Engineering Mechanics, vol.12, issue.4, pp.197-321, 1997.
DOI : 10.1016/S0266-8920(97)00003-9

A. C. Cornell, First order uncertainty analysis of soils deformation and stability, Lumb [47], pp.129-144

R. G. Ghanem and P. D. Spanos, Stochastic Finite Elements: A Spectral Approach, 1991.
DOI : 10.1007/978-1-4612-3094-6

´. E. Savin and D. Clouteau, Elastic wave propagation in a 3-D unbounded random heterogeneous medium coupled with a bounded medium. Application to seismic soil-structure interaction (SSSI), International Journal for Numerical Methods in Engineering, vol.125, issue.4, pp.607-630, 2002.
DOI : 10.1002/nme.442

URL : https://hal.archives-ouvertes.fr/hal-00273477

C. Soize, A nonparametric model of random uncertainties for reduced matrix models in structural dynamics, Probabilistic Engineering Mechanics, vol.15, issue.3, pp.277-294, 2000.
DOI : 10.1016/S0266-8920(99)00028-4

URL : https://hal.archives-ouvertes.fr/hal-00686293

C. Soize, Maximum entropy approach for modeling random uncertainties in transient elastodynamics, The Journal of the Acoustical Society of America, vol.109, issue.5, pp.1979-1996, 2001.
DOI : 10.1121/1.1360716

URL : https://hal.archives-ouvertes.fr/hal-00686287

C. Soize, Nonlinear dynamical systems with nonparametric model of random uncertainties, Uncertainties in Engineering Mechanics, vol.1, issue.1, pp.1-38, 2001.

C. Soize, Uncertain Dynamical Systems in the Medium-Frequency Range, Journal of Engineering Mechanics, vol.129, issue.9, pp.1017-1027, 2003.
DOI : 10.1061/(ASCE)0733-9399(2003)129:9(1017)

URL : https://hal.archives-ouvertes.fr/hal-00686212

C. Soize and H. Chebli, Random Uncertainties Model in Dynamic Substructuring Using a Nonparametric Probabilistic Model, Journal of Engineering Mechanics, vol.129, issue.4, pp.449-457, 2003.
DOI : 10.1061/(ASCE)0733-9399(2003)129:4(449)

URL : https://hal.archives-ouvertes.fr/hal-00686215

H. Chebli and C. Soize, Experimental validation of a nonparametric probabilistic model of nonhomogeneous uncertainties for dynamical systems, The Journal of the Acoustical Society of America, vol.115, issue.2, pp.697-705, 2004.
DOI : 10.1121/1.1639335

URL : https://hal.archives-ouvertes.fr/hal-00686209

C. Desceliers, C. Soize, and S. Cambier, Non-parametric???parametric model for random uncertainties in non-linear structural dynamics: application to earthquake engineering, Earthquake Engineering & Structural Dynamics, vol.33, issue.3, pp.315-327, 2003.
DOI : 10.1002/eqe.352

URL : https://hal.archives-ouvertes.fr/hal-00686208

M. Arnst, D. Clouteau, and M. Bonnet, Identification of probabilistic structural dynamics model: application to Soize's nonparametric model, Soize and Schuëller [31], pp.823-828

C. Soize, Random matrix theory for modeling uncertainties in computational mechanics, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.12-16, pp.1333-1366, 2005.
DOI : 10.1016/j.cma.2004.06.038

URL : https://hal.archives-ouvertes.fr/hal-00686187

R. Ohayon and C. Soize, Structural Acoustics and Vibration, The Journal of the Acoustical Society of America, vol.109, issue.6, 1998.
DOI : 10.1121/1.1352086

URL : https://hal.archives-ouvertes.fr/hal-00689039

R. Dautray and J. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, 1990.

J. P. Wolf and A. Paronesso, Lumped-parameter model for a rigid cylindrical foundation embedded in a soil layer on rigid rock, Earthquake Engineering & Structural Dynamics, vol.5, issue.12, pp.1021-1038, 1992.
DOI : 10.1002/eqe.4290211201

L. B. Pierce, Hardy functions, Junior paper, 2001.

H. A. Kramers, La diffusion de lalumì ere par les atomes, Resoconto del Congresso Internazionale dei Fisíci, pp.545-557, 1927.

R. D. Kronig, On the Theory of Dispersion of X-Rays, Journal of the Optical Society of America, vol.12, issue.6, pp.547-557, 1926.
DOI : 10.1364/JOSA.12.000547

D. C. Champeney, Fourier transforms and their applications of Techniques of physics, 1973.

A. Dienstfrey and L. Greengard, Analytic continuation, singular-value expansions, and Kramers-Kronig analysis, Inverse Problems, vol.17, issue.5, pp.1307-1320, 2001.
DOI : 10.1088/0266-5611/17/5/305

F. Chabas and C. Soize, Modeling mechanical subsystems by boundary impedance in the finite element method, La Recherche Aérospatiale, vol.5, pp.59-75, 1987.
URL : https://hal.archives-ouvertes.fr/hal-00770383

M. L. Mehta, Random matrices, 1991.

C. E. Shannon, A mathematical theory of communication, The Bell System Technical, Journal, vol.27, pp.379-423, 1948.

E. T. Jaynes, Information Theory and Statistical Mechanics, Physical Review, vol.106, issue.4, pp.620-630, 1957.
DOI : 10.1103/PhysRev.106.620

R. J. Allemang and D. L. Brown, A UNIFIED MATRIX POLYNOMIAL APPROACH TO MODAL IDENTIFICATION, Journal of Sound and Vibration, vol.211, issue.3, pp.301-322, 1998.
DOI : 10.1006/jsvi.1997.1321

P. Guillaume, R. Pintelon, and J. Schoukens, Parametric identification of multivariable systems in the frequency domain -a survey, Proceedings of the 21st International Conference on Noise and Vibration Engineering (ISMA), pp.1069-1082, 1996.

R. Pintelon and J. Schoukens, System identification: a frequency domain approach, 2001.

M. Van-barel and A. , A parallel algorithm for discrete least squares rational approximation, Numerische Mathematik, vol.33, issue.6, pp.99-121, 1992.
DOI : 10.1007/BF01385850

M. Van-barel and A. , Discrete least squares approximation with polynomial vectors, 1993.

R. Pintelon, Y. Rolain, A. Bultheel, and M. Van-barel, Frequency domain identification of multivariable systems using vector orthogonal polynomials, Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems, 2004.

C. K. Sanathanan and J. Koerner, Transfer function synthesis as a ratio of two complex polynomials, IEEE Transactions on Automatic Control, vol.8, issue.1, pp.56-58, 1963.
DOI : 10.1109/TAC.1963.1105517

A. Bultheel, A. Cuyt, W. Van-assche, M. Van-barel, and B. Verdonk, Generalizations of orthogonal polynomials, Journal of Computational and Applied Mathematics, vol.179, issue.1-2, pp.57-95, 2005.
DOI : 10.1016/j.cam.2004.09.036

A. Bultheel, M. Van-barel, and P. Van-gucht, Orthogonal basis functions in discrete least-squares rational approximation, Journal of Computational and Applied Mathematics, vol.164, issue.165, pp.164-165, 2004.
DOI : 10.1016/S0377-0427(03)00497-7

M. Arnst, D. Clouteau, H. Chebli, R. Othman, and G. Degrande, A non-parametric probabilistic model for ground-borne vibrations in buildings, Probabilistic Engineering Mechanics, vol.21, issue.1, pp.18-34, 2005.
DOI : 10.1016/j.probengmech.2005.06.004

URL : https://hal.archives-ouvertes.fr/hal-00018949

J. Sieffert and F. Cevaer, Handbook of impedance functions. Surface foundations, OuestÉditionsOuest´OuestÉditions, 1992.

T. Takagi, On an algebraic problem related to an analytic theorem of Carath??odory and Fej??r and on an allied theorem of Landau, Japanese Journal of Mathematics, vol.1, pp.83-93, 1925.
DOI : 10.1007/978-4-431-54995-6_19

P. Lumb, Statistics and Probability in Civil Engineering, Proceedings of the 1st International Conference on Applications of Statistics and Probability to Soil and Structural Engineering (ICASP) List of Figures C.1 Setting of the problem : bounded structure ? s , unbounded domain ? and coupling boundary, p.35, 1971.

. C. Fig, Real and imaginary parts of the shaking-rocking coupling element of the impedance matrix: condensation of the FEM-BEM model (solid line), condensation of the hidden variables model (dashed line), 0.95-confidence bounds for the 1000

. C. Fig, Real and imaginary parts of the shaking-pumping coupling element of the impedance matrix: condensation of the FEM-BEM model (solid line), condensation of the hidden variables model (dashed line), 0.95-confidence bounds for the 1000