Abstract
In this article we show that, given a Haar-type wavelet series { fj } in with respect to a dilation matrix A and tile Q, we can construct another Haar-type wavelet series in ℝ and tile in such a way that the stochastic processes defined by { fj } and on the probability spaces and , respectively, have the same finite-dimensional distributions. Thus, many properties of { fj } can be deduced from . This is a technique that, to our knowledge, has not been used in the literature. We show the power of this method by extending some known results for Haar series in ℝ to Haar-type wavelet series in with respect to a dilation matrix A, using simple proofs.
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