On limit laws for sums of Pfeifer records (Q1003312)

Asymptotic normality is demonstrated for centered and normalized sums of the form \( w_n=\sum_{i=0}^n \psi\left(\sum_{j=0}^i\beta_j X_j\right) \), where \(X_j\) are i.i.d. non-negative r.v.s with finite moment generating function, \(\beta_j\) are positive constants, and \(\psi\) is a non-decreasing regularly varying function. This result is applied to the sums of Pfeifer records, i.e., records in initial observations which are i.i.d. with common survival function \((\bar F_0)^{\alpha_0}\) before the first record and with the survival function \((\bar F_0)^{\alpha_n}\), \(n=1,2,\dots\), at the intervals between the \(n\)-th and \(n+1\)-th records.