On the moment-transfer approach for random variables satisfying a one-sided distributional recurrence. (English) Zbl 1227.05121
Summary: The moment-transfer approach is a standard tool for deriving limit laws of sequences of random variables satisfying a distributional recurrence. However, so far the approach could not be applied to certain “one-sided” recurrences with slowly varying moments and normal limit law. In this paper, we propose a modified version of the moment-transfer approach which can be applied to such recurrences. Moreover, we demonstrate the usefulness of our approach by re-deriving several recent results in an almost automatic fashion.
MSC:
05C05 | Trees |
05C80 | Random graphs (graph-theoretic aspects) |
60F05 | Central limit and other weak theorems |
68Q87 | Probability in computer science (algorithm analysis, random structures, phase transitions, etc.) |