Synthesis of two-dimensional fractional brownian motion via circulant embedding

Danudirdjo, Donny; Hirose, Akira

doi:10.1109/icip.2011.6115614

Cited by 2 publications

(1 citation statement)

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“…However, simulation of a vector random field is difficult and time consuming when the field is intrinsically stationary but not second-order stationary, because the direct and cross variograms might be unbounded and the cross-covariance matrix is not well defined. Several exact and approximate simulation methods have been proposed, for example, circulant embedding (Stein 2002;Danudirdjo and Hirose 2011), spectral representations (Arroyo and Emery 2017) and turning bands (Emery 2008). More recently, Moreva and Schlather (2018) proposed extensions of the cut-off circulant embedding approach for fast and exact simulation of univariate and bivariate Gaussian random fields.…”

Section: Discussionmentioning

confidence: 99%

Parametric variogram matrices incorporating both bounded and unbounded functions

Chen

Genton

2019

Stoch Environ Res Risk Assess

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We construct a flexible class of parametric models for both traditional and pseudo variogram matrix (valued functions), where the off-diagonal elements are the traditional cross variograms and pseudo cross variograms, respectively, and the diagonal elements are the direct variograms, based on the method of latent dimensions and the linear model of coregionalization. The entries in the parametric variogram matrix allow for a smooth transition between boundedness and unboundedness by changing the values of parameters, and thus between joint second-order and intrinsically stationary vector random fields, or between multivariate geometric Gaussian processes and multivariate Brown-Resnick processes in spatial extreme analysis. Keywords bounded and unbounded variogram • cross variogram • intrinsic stationarity • second-order stationarity • variogram matrix

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