Reciprocal processes on a tree-modeling and estimation issues

Motivated by multiresolution decomposition methods such as the discrete wavelet transformation, the authors introduce reciprocal processes on truncated N-ary trees. The authors discuss the relationship between such processes and nearest neighbor models. The authors show that they can derive a recursive description of the process, and that all reciprocal processes on N-ary trees reduce to autoregressive processes in the case of zero-valued boundary values at the bottom of the tree, corresponding to truncation of the tree. The authors then study the smoothing equations associated with such models