Exact simulation of some operator scaling Gaussian random fields

Date(s) : 19/02/2018   iCal
14 h 00 min - 15 h 00 min

Operator-scaling random fields, introduced in Bierm e, et al.. (2007) [Operator scaling stable random elds. Stoch. Proc. Appl., 117(3),312–332], satisfy an anisotropic self-similarity property, which extends the classical self-similarity property. Hence they generalize the fractional Brownian field, which is the most famous isotropic Gaussian self-similar random field. Up to now, to our best knowledge, such fields have only been defined through integral representations and their covariance functions are not known explicitly.
Hence only approximate methods as spectral methods can be used to simulate them. In this talk we then introduce some operator Gaussian random fields with covariance defined as anisotropic deformations of the fractional Brownian field covariance and with stationary increments. This allows us to propose a fast and exact method of simulation based on the circulant embedding matrix method, following ideas of Stein 2002 [Fast and exact simulation of fractional Brownian surfaces. Journal of Computational and Graphical Statistics, 11(3),587–599] for fractional Brownian surfaces syntheses.
This is a joint work with Hermine Bierme, Poitiers University (France).


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