Characterization of Multi-scale Invariant Random Fields
share
Applying certain flexible geometric sampling of a multi-scale invariant (MSI) field we provide a multi-dimensional multi-selfsimilar field which has a one to one correspondence with such sampled MSI field. This sampling enables us to characterize harmonic-like representation and spectral density function of the sampled MSI field. Imposing Markov property for the MSI field, we find that the covariance function and spectral density matrix of such sampled Markov MSI field are characterized by the covariance functions of samples of the first scale rectangle. We present an example of MSI field as two-dimensional simple fractional Brownian motion. We consider a real data example of the precipitation in some area of Brisbane in Australia for some special period. We show that precipitation on this area has MSI property and estimate time dependent scale and Hurst parameters of this MSI field in three dimension as latitude, longitude and time. Our method enables one to predict precipitation in time and place.
READ FULL TEXT