P. A. Ferreira, Modelling and Prediction of the Dynamic Behaviour of Railway Infrastructures at very high Speeds, 2010.

J. Chaolong, X. Weixiang, W. Futian, and W. Hanning, Track Irregularity Time Series Analysis and Trend Forecasting, Discrete Dynamics in Nature and Society, pp.10-1155, 2012.

J. Andrews, D. Prescott, and F. , A stochastic model for railway track asset management, Reliability Engineering & System Safety, vol.130, pp.76-84, 2014.
DOI : 10.1016/j.ress.2014.04.021

P. A. Ferreira and A. Lopez-pita, Numerical modelling of high speed train/track system for the reduction of vibration levels and maintenance needs of railway tracks, Construction and Building Materials, vol.79, pp.14-21, 2015.
DOI : 10.1016/j.conbuildmat.2014.12.124

N. Lestoille, C. Soize, G. Perrin, and C. Funfschilling, Long time evolution of train dynamics with respect to track geometry, The Second International Conference on Railway Technology: Research, Development and Maintenance, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00989424

N. Lestoille, C. Soize, and C. Funfschilling, Sensitivity of train stochastic dynamics to long-term evolution of track irregularities, Vehicle System Dynamics, vol.802, issue.5
DOI : 10.1007/978-90-481-3520-2

G. Perrin, C. Soize, D. Duhamel, and C. Funfschilling, Identification of Polynomial Chaos Representations in High Dimension from a Set of Realizations, SIAM Journal on Scientific Computing, vol.34, issue.6, pp.2917-2945, 2012.
DOI : 10.1137/11084950X
URL : https://hal.archives-ouvertes.fr/hal-00770006

G. Perrin, C. Soize, D. Duhamel, and C. Funfschilling, Track irregularities stochastic modeling, Track irregularities stochastic modeling, pp.123-130, 2013.
DOI : 10.1016/j.probengmech.2013.08.006
URL : https://hal.archives-ouvertes.fr/hal-00850645

G. Perrin, C. Soize, D. Duhamel, and C. Funfschilling, Quantification of the influence of the track geometry variability on the train dynamics, Mechanical Systems and Signal Processing, pp.60-61
DOI : 10.1016/j.ymssp.2015.01.004
URL : https://hal.archives-ouvertes.fr/hal-01137530

N. Lestoille, C. Soize, and C. Funfschilling, Stochastic modeling of train dynamics under effect of track irregularities and experimental comparisons, International Conference on Uncertainty in Structural Dynamics, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01066571

C. Soize, Identification of high-dimension polynomial chaos expansions with random coefficients for non-Gaussian tensor-valued random fields using partial and limited experimental data, Computer Methods in Applied Mechanics and Engineering, vol.199, pp.33-36, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00684324

G. Perrin, Random fields and associated statistical inverse problems for uncertainty quantifications -Applications to railway track geometries for high-speed trains dynamical responses and risk assessment, 2013.

G. Perrin, C. Soize, D. Duhamel, and C. Funfschilling, Karhunen???Lo??ve expansion revisited for vector-valued random fields: Scaling, errors and optimal basis., Journal of Computational Physics, vol.242, pp.607-622, 2013.
DOI : 10.1016/j.jcp.2013.02.036

G. Perrin, C. Soize, D. Duhamel, and C. Funfschilling, A Posteriori Error and Optimal Reduced Basis for Stochastic Processes Defined by a Finite Set of Realizations, SIAM/ASA Journal on Uncertainty Quantification, vol.2, issue.1, pp.745-762, 2014.
DOI : 10.1137/130905095
URL : https://hal.archives-ouvertes.fr/hal-01097139

C. Soize, Stochastic Models of Uncertainties in Computational Mechanics
DOI : 10.1061/9780784412237
URL : https://hal.archives-ouvertes.fr/hal-00749201

R. Ghanem and P. D. Spanos, Stochastic Finite Elements: A Spectral Approach , rev, 2003.
DOI : 10.1007/978-1-4612-3094-6

O. Le-maitre and O. Knio, Spectral Methods for Uncertainty Quantification, 2010.
DOI : 10.1007/978-90-481-3520-2

M. B. Priestley, The Spectral Analysis of Time Series., Journal of the Royal Statistical Society. Series A (Statistics in Society), vol.151, issue.3, 1981.
DOI : 10.2307/2983035

J. D. Hamilton, Time Series Analysis, 1994.

M. B. Priestley, Non-linear and non-stationary time series analysis, 1988.

R. Dahlhaus, Fitting time series models to nonstationary processes, The annals of statistics, pp.1-37, 1997.

B. Pfaff, Analysis of integrated and cointegrated time series with R, 2008.
DOI : 10.1007/978-0-387-75967-8

B. P. Carlin and T. A. Louis, Bayesian Methods for Data Analysis, 2009.

A. C. Harvey and . Forecasting, Structural Time Series Models and the Kalman Filter, 1989.

G. Evensen, Data Assimilation: The Ensemble Kalman Filter, 2009.
DOI : 10.1007/978-3-642-03711-5