Kevei, Péter and Terhesiu, D. (2019) Darling–Kac Theorem for Renewal Shifts in the Absence of Regular Variation. JOURNAL OF THEORETICAL PROBABILITY. ISSN 0894-9840
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Abstract
Regular variation is an essential condition for the existence of a Darling–Kac law. We weaken this condition assuming that the renewal distribution belongs to the domain of geometric partial attraction of a semistable law. In the simple setting of one-sided null recurrent renewal chains, we derive a Darling–Kac limit theorem along subsequences. Also in this context, we determine the asymptotic behaviour of the renewal function and obtain a Karamata theorem for positive operators. We provide several examples of dynamical systems to which these results apply.
| Item Type: | Article |
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| Additional Information: | Export Date: 19 September 2019 Correspondence Address: Kevei, P.; MTA-SZTE Analysis and Stochastics Research Group, Bolyai Institute, Aradi vértanúk tere 1, Hungary; email: kevei@math.u-szeged.hu |
| Uncontrolled Keywords: | Semistable law; Darling–Kac law; Gibbs–Markov map; Renewal theorem; |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 13 Sep 2020 06:25 |
| Last Modified: | 31 Dec 2021 00:16 |
| URI: | http://real.mtak.hu/id/eprint/113051 |
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