Open Access
January, 1987 On Subordinated Distributions and Generalized Renewal Measures
Rudolf Grubel
Ann. Probab. 15(1): 394-415 (January, 1987). DOI: 10.1214/aop/1176992278


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.


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Rudolf Grubel. "On Subordinated Distributions and Generalized Renewal Measures." Ann. Probab. 15 (1) 394 - 415, January, 1987.


Published: January, 1987
First available in Project Euclid: 19 April 2007

zbMATH: 0613.60007
MathSciNet: MR877612
Digital Object Identifier: 10.1214/aop/1176992278

Primary: 60E05
Secondary: 60K05

Keywords: asymptotic expansions , renewal measures , Subordinated distributions , tail behaviour

Rights: Copyright © 1987 Institute of Mathematical Statistics

Vol.15 • No. 1 • January, 1987
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