MRA of processes synthesized by differintegration

In this paper a definition of multiresoltuion 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 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.