Simulation of Sample Paths of Non Gaussian Stationary Random Fields
Mathematical justifications are given for a simulation technique of multivariate nonGaussian random processes and fields based on Rosenblatt-s transformation of Gaussian processes. Different types of convergences are given for the approaching sequence. Moreover an original numerical method is proposed in order to solve the functional equation yielding the underlying Gaussian process autocorrelation function.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1330473Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1460
 Monbet V., Aillot P., and Prevosto M. Survey of stochastic models for wind and sea state time series. Prob. Eng. Mech., 22:113-126, 2007.
 Monbet V. and Prevosto M. Bivariate of non stationary and non gaussian observed processes.application to sea state parameters. Applied Ocean Research, 23:139-145, 2007.
 Fouques S., Myrhaug D., and Nielsen M. Seasonal modeling of multivariate distributions of metocean parameters with application to marine operations. J. Offshore mech. Artc., 126:202-212, 2004.
 Gusev A. Peak factors of mexican accelerograms: Evidence of a nongaussian amplitude distribution. J. Geophys. Res., 101(B9):20083-20090, 1996.
 Grigoriu M. and Kafali G. Non-Gaussian model for spatially coherent seismic ground motions. In Der Kureghian Madanat and Pestanat. , editors, Application of Staistics and probablity in Civil Engineering. Millpress, 2003.
 Nielsen M., Larsen G., and Hansen K. Simulation of inhomogeneous, non-stationary and non-gaussian turbulentwinds. J. of Physics: Conference series 75, 75:1-9, 2007.
 Nielsen M., H├©jstrup J., Hansen K., and Thesberg L. Validity of the assumption of Gaussian turbulence. In Proceedings of the European Wind Energy Conference, Denmark, July 2001.
 Rocha G. and al. . Simulation of non-gaussian cosmic microwave background maps. Mon. Not. R. Astron. Soc., 357:1-11, 2005.
 Grigoriu M. Simulation of stationary non-gaussian translation processes. j. of Eng. Mech. ASCE, 124(2):pp12-127, 1998.
 Gurley K. and Kareem A. Simulation of non-gaussian processes. In Spanos , editor, Computational Stochastic Mechanics, CSM98, pages pp 11-21, Rotterdam, 1999. Balkema.
 IASSAR(Report) . A state-of-the-art report on computational stochastic mechanics. In Shinozuka M. and Spanos P.D., editors, Probabilistic Engineering Mechanics, volume 12(4), pages 197-321, 1997.
 Poirion F. Numerical simulation of homogeneous non-Gaussian random vector fields. J. of Sound and Vibration, 160(1):25-42, 1993.
 Popescu R., Deodatis G., and Prevost J.H. Simulation of homogeneous nongaussian stochastic vector fields. Prob. Eng. Mech, 13(1):1-13, 1998.
 Sakamoto S. and Ghanem R. Simulation of non-Gaussian fields with the Karhunen-Loeve and polynomial chaos expansions. In Engineering Mechanics Conference, Baltimore (USA), June 1999.
 Sakamoto S. and Ghanem R. Simulation of multi-dimensinal non- Gaussian non-stationary random fields. Probabilistic Engineering Mechanics, 17(2):167-176, 2002.
 Li L.B., Phoon K.K., and Quck S.T. Comparison between karhunen-love expansion and translation-based simulation of non-gaussian processes. Computers and Structures, 85:264-276, 2007.
 Puig B., Poirion F., and Soize C. Non-gaussian simulation using hermite polynomial expansion: convergences and algorithms. Prob. Eng. Mech., 17(3):253-264, 2002.
 Poirion, F and Puig, B White noise and simulation of ordinary Gaussian processes. Monte Carlo Methods and Appl., 10(1): 9-89,2004.
 Devroye L. Non Uniform Random Variate Generation. Springer-Verlag, New-York, 1986.
 Rosenblatt M. Remarks on a multivariate transformation. Ann. Math., 23:470-472, 1952.
 Rubinstein R.Y. Simulation And The Monte Carlo Method. John Wiley & Sons, 1981.
 Luciano Elisa, Vecchiato Walter, and Cherubini Umberto. Copula Methods in Finance. Wiley, John & Sons, Incorporated, 2004.
 Xiaohong C., Wu W., and Yanping Y. Efficient estimation of copulabased semiparametric markov models, 2009.
 Brdossy A. and Li Y. Geostatistical interpolation using copulas. Water Resour. Res., 44, 2008.
 Yan-Heng Li, Bao-ping Shi, and Jian Zhang. Copula joint function and its application in probability seismic hazard analysis. Acta Seismologica Sinica, 21(3):296-305, 2008.
 Nelsen R. An Introduction to Copulas. Springer Series In Statistics. Springer, 2006.