×

An optimality result about sample path properties of operator scaling Gaussian random fields. (English) Zbl 1389.60053

Summary: We study the sample paths properties of operator scaling Gaussian random fields. Such fields are anisotropic generalizations of anisotropic self-similar random fields as anisotropic fractional Brownian motion. Some characteristic properties of the anisotropy are revealed by the regularity of the sample paths. The sharpest way of measuring smoothness is related to these anisotropies and thus to the geometry of these fields.

MSC:

60G17 Sample path properties
60G15 Gaussian processes
60G18 Self-similar stochastic processes
60G60 Random fields
60G22 Fractional processes, including fractional Brownian motion
PDFBibTeX XMLCite
Full Text: arXiv