Let $(X_k)_{k\in\mathbb{N}}$ be a sequence of i.i.d. random variables with partial sums $S_0 = 0, S_n = \sum^n_{k=1} X_k$. We investigate the behaviour of $\sum^\infty_{n=0} a_nP(S_n \in x + A)$ as $x \rightarrow \pm \infty$, where $(a_n)_{n\in\mathbb{N}_0}$ is a sequence of nonnegative numbers and $A \subset \mathbb{R}$ is a fixed Borel set.
@article{1176992278,
author = {Grubel, Rudolf},
title = {On Subordinated Distributions and Generalized Renewal Measures},
journal = {Ann. Probab.},
volume = {15},
number = {4},
year = {1987},
pages = { 394-415},
language = {en},
url = {http://dml.mathdoc.fr/item/1176992278}
}
Grubel, Rudolf. On Subordinated Distributions and Generalized Renewal Measures. Ann. Probab., Tome 15 (1987) no. 4, pp. 394-415. http://gdmltest.u-ga.fr/item/1176992278/