Multifractality in space-time statistical models

摘要

This paper introduces two families of space-time random models with multifractal spatial characteristics, respectively generated in continuous and discrete time, and both defined on multifractal spatial domains. The definition of the first class is given in terms of a Feller semigroup generated by a pseudodifferential operator of variable order. In the second case, the spatial process at time t + 1 is obtained by applying a variable order blurring operator to the spatial process at time t and adding the innovation given by a spatiotemporal process uncorrelated in time. Spatial multi-fractal properties of the two classes of space-time processes introduced are analyzed. The implementation of space-time filtering and prediction techniques is also discussed.