Multi-scale representation of stochastic processes using compactly supported wavelets

Compactly supported wavelets are used to obtain multiscale representations of second-order stochastic processes. In the case of second-order orthogonal increment processes, decorrelation of the wavelet coefficients can be achieved if the time localizations are sufficiently far apart, and precise conditions are given in relation to the support of the wavelets. An expression for the correlation structure of the coefficients is also given. It is shown that for certain classes of second-order processes the correlation along scales decays exponentially for all pairs of coefficients. The relation of such representations to multiresolution models on trees proposed by M. Basseville et al. (1992) is studied