Simulation of non-Gaussian multivariate stationary processes

Abstract Mathematical justifications are given for a simulation technique of multivariate non-Gaussian 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.

[1]  Christian Soize,et al.  Non-Gaussian simulation using Hermite polynomial expansion: convergences and algorithms , 2002 .

[2]  M. Hobson,et al.  Simulation of non-Gaussian cosmic microwave background maps , 2005 .

[3]  G. Schuëller.  A state-of-the-art report on computational stochastic mechanics , 1997 .

[4]  R. Nelsen.  An Introduction to Copulas , 1998 .

[5]  F. Poirion.  Numerical Simulation Of Homogeneous Non-Gaussian Random Vector Fields , 1993 .

[6]  L. Devroye.  Non-Uniform Random Variate Generation , 1986 .

[7]  K. Phoon,et al.  Comparison between Karhunen-Loève expansion and translation-based simulation of non-Gaussian processes , 2007 .

[8]  Finn Gunnar Nielsen,et al.  Seasonal Modeling of Multivariate Distributions of Metocean Parameters With Application to Marine Operations , 2004 .

[9]  M. Rosenblatt.  Remarks on a Multivariate Transformation , 1952 .

[10]  A. Bárdossy,et al.  Geostatistical interpolation using copulas , 2008 .

[11]  George Deodatis,et al.  Simulation of homogeneous nonGaussian stochastic vector fields , 1998 .

[12]  Michael Havbro Faber,et al.  Applications of Statistics and Probability in Civil Engineering , 2011 .

[13]  Jian Zhang,et al.  Copula joint function and its application in probability seismic hazard analysis , 2008 .

[14]  Reuven Y. Rubinstein,et al.  Simulation and the Monte Carlo method , 1981, Wiley series in probability and mathematical statistics.

[15]  A. A. Gusev,et al.  Peak factors of Mexican accelerograms: Evidence of a non-Gaussian amplitude distribution , 1996 .

[16]  E. Luciano,et al.  Copula methods in finance , 2004 .

[17]  Marc Prevosto,et al.  Survey of stochastic models for wind and sea state time series , 2007 .

[18]  Roger Ghanem,et al.  Simulation of multi-dimensional non-gaussian non-stationary random fields , 2002 .

[19]  Morten Nielsen,et al.  Simulation of inhomogeneous, non-stationary and non-Gaussian turbulent winds , 2007 .

[20]  Xiaohong Chen,et al.  Efficient Estimation of Copula-Based Semiparametric Markov Models , 2009 .

[21]  Marc Prevosto,et al.  Bivariate simulation of non stationary and non Gaussian observed processes: Application to sea state parameters , 2000 .

[22]  M. Grigoriu.  Simulation of stationary non-Gaussian translation processes , 1998 .