Multiscale autoregressive processes. II. Lattice structures for whitening and modeling

摘要

For pt.I see ibid., vol.40, no.8, p.1915-34 (1992). Lattice structures for the whitening and modeling of isotropic processes on trees are developed, and a result relating the stability properties of these models to the reflection coefficient sequence introduced in pt.I is presented. This framework allows one to obtain a detailed analysis of the Wold decomposition of processes on trees. One interesting aspect of this is that there is a significantly larger class of singular processes on dyadic trees than on the integers.