Standard transition matrix

Abstract

According to Theorem 1.3, the analytic study of (p _ij ) is reduced to that of (П _IJ if the set of indices F is ignored. In fact, the curtailed matrix (p _ij ), i, j∈I – F, is a transition matrix and its elements differ from those of П _IJ only in certain constant factors depending on the second index. From the standpoint of probability, it will be seen (in § 4) that the set F plays a nuisance role and can indeed be ignored. Moreover, the reduction from (P _ij ) to (П _IJ is also justified on probabilistic grounds (see Theorem 4.3). The distinctive feature of the transition matrix (П _IJ ) is the property (1.14) which will now be formulated as a definition.