Abstract
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 multifractal properties of the two classes of space–time processes introduced are analyzed. The implementation of space–time filtering and prediction techniques is also discussed.
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Acknowledgments
This work has been partially supported by projects BFM2002-01836 and MTM2005-08597 of the DGI, and P05-FQM-00990 of the Andalousian CICE, Spain, and ARC grant A69804041 and NSF CMG grant 0417676.
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Ruiz-Medina, M.D., Angulo, J.M. & Anh, V.V. Multifractality in space–time statistical models. Stoch Environ Res Risk Assess 22 (Suppl 1), 81–86 (2008). https://doi.org/10.1007/s00477-007-0155-9
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DOI: https://doi.org/10.1007/s00477-007-0155-9