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- Title
Rates of convergence for renewal sequences in the null-recurrent case.
- Authors
Isaac, Richard
- Abstract
Motivated by work of Garsia and Lamperti we consider null-recurrent renewal sequences with a regularly varying tail and seek information about their rate of convergence to zero. The main result shows that such sequences subject to a monotonicity condition obey a limit law whatever the value of the exponent α is, 0 < α < 1. This monotonicity property is seen to hold for a large class of renewal sequences, the so-called Kaluza sequences. This class includes moment sequences, and therefore includes the sequences generated by reversible Markov chains. Several subsidiary results are proved.
- Publication
Journal of the Australian Mathematical Society, 1988, Vol 45, Issue 3, p381
- ISSN
1446-7887
- Publication type
Article
- DOI
10.1017/S1446788700031098