A law of large numbers for the bifurcating autoregressive process

The bifurcating autoregressive model is of both practical interest, as in the analysis of cell lineage data in Huggins & Staudte, and of theoretical interest in that whilst each line of descent is a first order autoregressive process the added complications when considering all lines of descent in a tree of data require new analytical techniques. Here laws of large numbers are given for several quantities associated with the bifurcating autoregressive process which are required to derive the asymptotic properties of both robust and maximum likelihood estimators.