In the context of countable groups polynomial volume growth, we consider a large class random walks that are allowed to take long jumps along multiple subgroups according power law distributions. For such walk, study time behavior its probability return at n in terms key parameters describing driving measure and structure underlying group. We obtain assorted estimates including near-diagonal tw...

Simple proofs of the continuity of the convolution of measures for certain topologies are presented. In addition, results on the compactness of probability measures and on infinite convolutions of probability measures are obtained.

Ethnography contributes to measure development by enhancing validity and providing a basis for qualitative validation. Validating research measures means making cases for their "trustworthiness." The authors argue for the trustworthiness of CONNECT, a measure of continuity of care, by presenting the interpretive logic through which they elaborated continuity for measure construction purposes. T...

This article presents a group-based method to jointly estimate developmental trajectories of 2 distinct but theoretically related measurement series. The method will aid the analysis of comorbidity and heterotypic continuity. Three key outputs of the model are (a) for both measurement series, the form of the trajectory of distinctive subpopulations; (b) the probability of membership in each suc...

1 Suppose we are given two probability measures on the set of one-way infinite finite-alphabet sequences. Consider the question when one of the measures predicts the other, that is, when conditional probabilities converge (in a certain sense), if one of the measures is chosen to generate the sequence. This question may be considered a refinement of the problem of sequence prediction in its most...