On stationarizability for nonstationary 2-D random fields using discrete wavelet transforms

Abstract

The emphasis in this correspondence is on the study of nonstationary two-dimensional (2-D) random fields with wide-sense stationary increments, wide-sense stationary jumps, and 2-D fractional Brownian motion (fBm) fields. The effort made in this work is to develop a realizable method of stationarization provided for nonstationary 2-D random fields. We also present the correlation functions of the discrete wavelet transform relating to 2-D fBm fields that will decay hyperbolically fast.