MRA of processes synthesized by differintegration

A definition of multiresolution analysis (MRA) of Gaussian processes is proposed. The problem, in a natural way, reduces to the MRA of the associated reproducing kernel Hilbert space. We then show that for processes synthesized from Gaussian white process by fractional integration of order α⩾1, this definition is applicable. The MRA results in an orthogonal expansion of these processes. The region of interest is the positive real line. Using this representation then a decomposition of a wider class of Gaussian processes is given. This representation is multiscale in two ways: firstly, the Gaussian process is split into various component processes characterized by the smoothness of their sample paths and secondly, each of these component processes has a MRA as defined in this paper