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.
"On the Moment-Transfer Approach for Random Variables Satisfying a One-Sided Distributional Recurrence." Electron. J. Probab. 16 903 - 928, 2011. https://doi.org/10.1214/EJP.v16-885