MRA of processes synthesized by fractional integration

摘要

In this correspondence, we show that the multiresolution analysis (MRA) of the reproducing kernel Hilbert space, associated with processes synthesized by fractional integration of white processes, leads to an orthogonal, multiresolution decomposition of the process. We show that the decomposition converges almost surely and uniformly on finite intervals. We also show that the random coefficients in the decomposition can be evaluated almost surely.