Journal article
Renorming divergent perpetuities
Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability, Vol.17(3), pp.880-894
01 Aug 2011
Abstract
We consider a sequence of random variables (R-n) defined by the recurrence R-n = Q(n) + MnRn-1, n >= 1, where Ro is arbitrary and (Q(n), M-n), n >= 1 , are i.i.d. copies of a two-dimensional random vector (Q, M), and (Q(n), M-n) is independent of Rn-1. It is well known that if Eln vertical bar M vertical bar <0 and Eln(+) vertical bar Q vertical bar < infinity, then the sequence (R-n) converges in distribution to a random variable R given by R (d) double under bar Sigma(infinity)(k=1) Q(k)Pi(k-1)(j=1), and usually referred to as perpetuity. In this paper we consider a situation in which the sequence (R-n) itself does not converge. We assume that Eln vertical bar M vertical bar exists but that it is non-negative and we ask if in this situation the sequence (R-n), after suitable normalization, converges in distribution to a non-degenerate limit.
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Details
- Title
- Renorming divergent perpetuities
- Creators
- Pawel Hitczenko - Drexel UniversityJacek Wesolowski - Warsaw Univ Sci & Technol, Wydzial Matemat & Nauk Informacyjnych, PL-00661 Warsaw, Poland
- Publication Details
- Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability, Vol.17(3), pp.880-894
- Publisher
- Int Statistical Inst
- Number of pages
- 15
- Grant note
- H98230-09-1-0062 / NSA; National Security Agency
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Identifiers
- 991019167865104721
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