A. M. Abbas and C. S. Manohar, Investigations into critical earthquake load models within deterministic and probabilistic frameworks, Earthquake Engineering & Structural Dynamics, vol.92, issue.4, pp.813-832, 2002.
DOI : 10.1002/eqe.124

S. M. Allam and T. K. Datta, Analysis of cable-stayed bridges under multi-component random ground motion by response spectrum method, Engineering Structures, pp.1367-1377, 2000.

J. G. Anderson and M. D. Trifunac, A note on probabilistic computation of earthquake response spectrum amplitudes, Nuclear Engineering and Design, vol.51, issue.2, pp.285-294, 1979.
DOI : 10.1016/0029-5493(79)90095-5

J. L. Beck and C. Papadimitriou, Moving resonance in nonlinear response to fully non-stationary stochastic ground motion, Probabilistic Engineering Mechanics, vol.8, pp.3-4157, 1993.

H. S. Chan, Earthquake response spectrum analysis of platforms engineering structures, Engineering Structures, pp.272-276, 1987.

Y. Q. Chen, Modification of floor response spectrum based on stochastic sensitivity analysis, Engineering Structures, pp.40-46, 1993.

T. F. Coleman and Y. Li, On the convergence of reflective newton methods for large-scale nonlinear minimization subject to sounds, Mathematical Programming, pp.189-224, 1994.

T. F. Coleman and Y. Li, An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds, SIAM Journal on Optimization, vol.6, issue.2, pp.418-445, 1996.
DOI : 10.1137/0806023

D. Kiureghian, A. Crempien, and J. , An evolutionary model for earthquake ground motion, Structural Safety, pp.235-246, 1989.

D. Kiureghian, A. Nakaruma, and Y. , CQC modal combination rule for high-frequency modes, Earthquake Engineering and Structural Dynamics, pp.943-956, 1993.

S. Geman and D. Geman, Stochastic relaxation, Gibbs distribution and the Bayesian distribution of images, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.6, pp.721-741, 1984.

J. Ghaboussi and C. C. Lin, New method of generating spectrum compatible accelerograms using neural networks, Earthquake Engineering & Structural Dynamics, vol.27, issue.4, pp.377-396, 1998.
DOI : 10.1002/(SICI)1096-9845(199804)27:4<377::AID-EQE735>3.0.CO;2-2

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

P. Gu and Y. K. Wen, A Record-Based Method for the Generation of Tridirectional Uniform Hazard-Response Spectra and Ground Motions Using the Hilbert-Huang Transform, Bulletin of the Seismological Society of America, vol.97, issue.5, pp.1539-1556, 2007.
DOI : 10.1785/0120060127

I. Gikhman and A. V. Skorokhod, The Theory of Stochastic Processes, 1979.
DOI : 10.1007/978-3-642-61921-2

A. K. Gupta and S. L. Chu, Probable simultaneous response by the response spectrum method of analysis, Nuclear Engineering and Design, vol.44, issue.1, pp.93-95, 1977.
DOI : 10.1016/0029-5493(77)90126-1

A. K. Gupta and J. W. Jaw, Response spectrum method for nonclassically damped systems, Nuclear Engineering and Design, vol.91, issue.2, pp.161-169, 1986.
DOI : 10.1016/0029-5493(86)90203-7

A. K. Gupta and J. W. Jaw, Coupled response spectrum analysis of secondary systems using uncoupled modal properties, Nuclear Engineering and Design, vol.92, issue.1, pp.61-68, 1986.
DOI : 10.1016/0029-5493(86)90099-3

A. K. Gupta and J. W. Jaw, A new instructure response spectrum (IRS) method for multiply connected secondary systems with coupling effects, Nuclear Engineering and Design, vol.96, issue.1, pp.63-80, 1986.
DOI : 10.1016/0029-5493(86)90162-7

I. D. Gupta and R. G. Joshi, An improved spectrum superposition method for structures with rigid modes, Nuclear Engineering and Design, vol.185, issue.2-3, pp.293-307, 1998.
DOI : 10.1016/S0029-5493(98)00235-0

I. D. Gupta and M. D. Trifunac, Defining equivalent stationary PSDF to account nonstationarity of earthquake ground motion, Soil Dynamics and Earthquake Engineering, pp.89-99, 1998.

A. H. Hadjian, Seismic response of structures by the response spectrum method, Nuclear Engineering and Design, vol.66, issue.2, pp.179-201, 1981.
DOI : 10.1016/0029-5493(81)90142-4

W. K. Hastings, Monte Carlo sampling methods using Markov chains and their applications, Biometrika, vol.57, issue.1, pp.57-97, 1970.
DOI : 10.1093/biomet/57.1.97

F. Jalayer and J. L. Beck, Effects of two alternative representations of ground-motion uncertainty on probabilistic seismic demand assessment of structures, Earthquake Engineering & Structural Dynamics, vol.83, issue.1, pp.61-79, 2008.
DOI : 10.1002/eqe.745

R. Jankowski, Pounding force response spectrum under earthquake excitation, Engineering Structures, pp.1149-1161, 2006.
DOI : 10.1016/j.engstruct.2005.12.005

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

K. Kanai, Seismic-empirical formula for the seismic characteristics of the ground, Bulletin of the Earthquake Research Institute, vol.35, pp.309-325, 1957.

M. R. Khan, Improved method of generation of artificial time-histories, rich in all frequencies, from floor spectra, Earthquake Engineering and Structural Dynamics, pp.985-992, 1987.

G. Kost, T. Tellkamp, and H. Kamil, Automated generation of spectrum-compatible artificial time histories, Nuclear Engineering and Design, vol.45, issue.1, pp.243-249, 1978.
DOI : 10.1016/0029-5493(78)90119-X

N. T. Lam, J. L. Wilson, and A. M. Chandler, Seismic displacement response spectrum estimated from the frame analogy soil amplification model, Engineering Structures, vol.23, issue.11, pp.1437-1452, 2001.
DOI : 10.1016/S0141-0296(01)00049-9

S. C. Lee and S. W. Han, Neural-network-based models for generating artificial earthquakes and response spectra, Computers & Structures, vol.80, issue.20-21, pp.1627-1638, 2002.
DOI : 10.1016/S0045-7949(02)00112-8

S. Levy and J. P. Wilkinson, Generation of artificial time-histories, rich in all frequencies, from given response spectra, Nuclear Engineering and Design, vol.38, issue.2, pp.241-251, 1976.
DOI : 10.1016/0029-5493(76)90099-6

J. H. Li and J. Li, A response spectrum method for seismic response analysis of structures under multi-support excitations, Structural Engineering and Mechanics, pp.255-273, 2005.

Y. K. Lin and Y. Yong, Evolutionary Kanai???Tajimi Earthquake Models, Journal of Engineering Mechanics, vol.113, issue.8, pp.1119-1137, 1987.
DOI : 10.1061/(ASCE)0733-9399(1987)113:8(1119)

B. Nouromid, J. L. Sackman, and A. Der-kiureghian, Modal characterization of equipment-continuous structure systems, Journal of Sound and Vibration, vol.88, issue.4, pp.459-472, 1983.
DOI : 10.1016/0022-460X(83)90649-1

D. Pachakis, L. S. Katafygiotis, and A. Zerva, Amplitude Variability in Simulated Incoherent Seismic Ground Motions, Journal of Engineering Mechanics, vol.133, issue.7, pp.844-848, 2007.
DOI : 10.1061/(ASCE)0733-9399(2007)133:7(844)

K. A. Peters, D. Schmitz, and U. Wagner, Determination of floor response spectra on the basis of the response spectrum method, Nuclear Engineering and Design, vol.44, issue.2, pp.255-262, 1977.
DOI : 10.1016/0029-5493(77)90032-2

H. J. Pradlwarter and G. I. Schueller, On advanced Monte Carlo simulation procedures in stochastic structural dynamics, International Journal of Non-Linear Mechanics, vol.32, issue.4, pp.735-744, 2003.
DOI : 10.1016/S0020-7462(96)00091-1

H. J. Pradlwarter, G. I. Schueller, and C. A. Schenk, A computational procedure to estimate the stochastic dynamic response of large non-linear FEmodels, Computer Methods in Applied Mechanics and Engineering, vol.192, pp.7-8, 2003.

A. Preumont, The generation of spectrum compatible accelerograms for the design of nuclear-power plants, Earthquake Engineering and Structural Dynamics, pp.481-497, 1984.

M. B. Priestley, Non-linear and Non-Stationary Time series analysis, 1988.

R. Y. Rubinstein, Simulation and the Monte Carlo Method, 1981.

F. Sabetta and A. Pugliese, Estimation of response spectra and simulation of non-stationary earthquake ground motions, pp.337-352, 1996.

H. Sato, M. Komazaki, and M. Ohori, An extensive study of a simple method for estimating the response spectrum based on a simulated spectrum, Nuclear Engineering and Design, vol.50, issue.3, pp.399-410, 1978.
DOI : 10.1016/0029-5493(78)90162-0

C. A. Schenk, H. J. Pradlwarter, and G. I. Schueller, Non-stationary response of large, non-linear finite element systems under stochastic loading, Computers & Structures, vol.83, issue.14, pp.83-1086, 2005.
DOI : 10.1016/j.compstruc.2004.11.018

R. J. Scherer, J. D. Riera, and G. I. Schueller, Estimation of the timedependent frequency content of earthquake accelerations, Nuclear Engineering and Design, issue.3, pp.71-301, 1982.

G. I. Schueller and H. J. Pradlwarter, On the stochastic response of nonlinear FE models, Archive of Applied Mechanics, pp.9-10, 1999.

G. I. Schueller, Computational stochastic mechanics ??? recent advances, Computers & Structures, vol.79, issue.22-25, pp.22-25, 2001.
DOI : 10.1016/S0045-7949(01)00078-5

G. I. Schueller, H. J. Pradlwarter, and C. A. Schenk, Non-stationary response of large linear FE models under stochastic loading, Computers & Structures, vol.81, issue.8-11, pp.8-11, 2003.
DOI : 10.1016/S0045-7949(02)00473-X

R. J. Serfling, Approximation Theorems of Mathematical Statistics, 1980.

C. E. Shannon, A Mathematical Theory of Communication, Bell System Technical Journal, vol.27, issue.3, pp.379-423, 1948.
DOI : 10.1002/j.1538-7305.1948.tb01338.x

A. M. Sharma and M. P. Singh, Floor spectra by mode acceleration-based response spectrum approach for nonclassically damped structures, Nuclear Engineering and Design, vol.92, issue.2, pp.181-193, 1986.
DOI : 10.1016/0029-5493(86)90245-1

S. Smith and B. Hollowell, A proposed method to standardize shock response spectrum (SRS) analysis -To provide agreement between tests performed at different facilities, Journal of the Institute of Environmental Sciences, vol.39, issue.3, pp.19-24, 1996.

C. Soize, The Fokker-Planck Equation for Stochastic Dynamical Systems and its Explicit Steady State Solutions, 1994.
DOI : 10.1142/2347

URL : https://hal.archives-ouvertes.fr/hal-00770411

C. Soize, Construction of probability distributions in high dimension using the maximum entropy principle: Applications to stochastic processes, random fields and random matrices, International Journal for Numerical Methods in Engineering, vol.195, issue.4, 2008.
DOI : 10.1002/nme.2385

URL : https://hal.archives-ouvertes.fr/hal-00684517

C. Soize and R. Ghanem, Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure, SIAM Journal on Scientific Computing, vol.26, issue.2, pp.395-410, 2004.
DOI : 10.1137/S1064827503424505

URL : https://hal.archives-ouvertes.fr/hal-00686211

J. C. Spall, Introduction to Stochastic Search and Optimization, 2003.
DOI : 10.1002/0471722138

P. D. Spanos, A. Giaralis, and N. P. Politis, Time???frequency representation of earthquake accelerograms and inelastic structural response records using the adaptive chirplet decomposition and empirical mode decomposition, Soil Dynamics and Earthquake Engineering, vol.27, issue.7, pp.27-675, 2007.
DOI : 10.1016/j.soildyn.2006.11.007

L. Su, S. L. Donga, and S. Kato, A new average response spectrum method for linear response analysis of structures to spatial earthquake ground motions, Engineering Structures, pp.28-1835, 2006.

H. Tajimi, A statistical method of determining the maximum response of a building structure during an earthquake, Proceedings of the 2nd World Conference on Earthquake Engineering, pp.782-797, 1960.

V. Totik, Orthogonal polynomials with respect to varying weights, Journal of Computational and Applied Mathematics, vol.99, issue.1-2, pp.373-385, 1998.
DOI : 10.1016/S0377-0427(98)00171-X

M. D. Trifunac, Brief history of earthquake response spectra, Soil Dynamics and Earthquake Engineering, pp.501-508, 2006.

J. F. Unruh and D. D. Kana, An iterative procedure for the generation of consistent power/response spectrum, Nuclear Engineering and Design, vol.66, issue.3, pp.427-435, 1981.
DOI : 10.1016/0029-5493(81)90172-2

J. N. Yang, S. Sarkani, and F. X. Long, A response spectrum approach for seismic analysis of nonclassically damped structure, Engineering Structures, pp.173-184, 1990.

C. H. Yeh and Y. K. Wen, Modeling of non-stationary ground motion and analysis of inelastic structural response, Structural Safety, pp.281-298, 1990.

A. Zerva and J. L. Beck, Identification of parametric ground motion random fields from spatially recorded seismic data, Earthquake Engineering and Structural Dynamics, pp.771-791, 2003.