---
res:
  bibo_abstract:
  - "We consider autoregressive sequences Xn = aXn−1 + ξn and\r\nMn = max{aMn−1 ,
    ξn} with a constant a ∈ (0, 1) and with positive, in-\r\ndependent and identically
    distributed innovations {ξk }. It is known that if\r\nP(ξ1 > x) ∼ d\r\nlog x with
    some d ∈ (0, − log a) then the chains {Xn} and {Mn}\r\nare null recurrent. We
    investigate the tail behaviour of recurrence times in this\r\ncase of logarithmically
    decaying tails. More precisely, we show that the tails\r\nof recurrence times
    are regularly varying of index −1 − d/ log a. We also prove\r\nlimit theorems
    for {Xn} and {Mn} conditioned to stay over a fixed level x0.\r\nFurthermore, we
    study tail asymptotics for recurrence times of {Xn} and {Mn}\r\nin the case when
    these chains are positive recurrent and the tail of log ξ1 is\r\nsubexponential.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Denis
      foaf_name: Denisov, Denis
      foaf_surname: Denisov
  - foaf_Person:
      foaf_givenName: Günter
      foaf_name: Hinrichs, Günter
      foaf_surname: Hinrichs
  - foaf_Person:
      foaf_givenName: Martin
      foaf_name: Kolb, Martin
      foaf_surname: Kolb
      foaf_workInfoHomepage: http://www.librecat.org/personId=48880
  - foaf_Person:
      foaf_givenName: Vitali
      foaf_name: Wachtel, Vitali
      foaf_surname: Wachtel
  bibo_doi: https://doi.org/10.48550/arXiv.2203.14772
  bibo_volume: 27
  dct_date: 2022^xs_gYear
  dct_language: eng
  dct_publisher: Institute of Mathematical Statistics@
  dct_title: Persistence of autoregressive sequences with logarithmic tails@
...