Abstract
This work is concerned with non-stationary 2D fields having stationary increments. The classical fractional Brownian motion model is limited in some applications, since it is isotropic and depends on a single parameter (the Hurst coefficient H). We introduce herein new models for possibly anisotropic textures, based on fractional orders of differencing in two orthogonal directions of space. Some of the properties of fields with fractional stationary increments are also discussed. We then focus on self-similar processes with stationary increments of order one and stress the role of the structure function in the study of these processes.
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