The Annals of Probability

On Subordinated Distributions and Generalized Renewal Measures

Rudolf Grubel

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Abstract

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 information

Source
Ann. Probab., Volume 15, Number 1 (1987), 394-415.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176992278

Digital Object Identifier
doi:10.1214/aop/1176992278

Mathematical Reviews number (MathSciNet)
MR877612

Zentralblatt MATH identifier
0613.60007

JSTOR
links.jstor.org

Subjects
Primary: 60E05: Distributions: general theory
Secondary: 60K05: Renewal theory

Keywords
Subordinated distributions renewal measures asymptotic expansions tail behaviour

Citation

Grubel, Rudolf. On Subordinated Distributions and Generalized Renewal Measures. Ann. Probab. 15 (1987), no. 1, 394--415. doi:10.1214/aop/1176992278. https://projecteuclid.org/euclid.aop/1176992278


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