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Slowly varying asymptotics for signed stochastic difference equations

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSNChapter (peer-reviewed)peer-review

Publication date1/12/2021
Host publicationA Lifetime of Excursions Through Random Walks and Lévy Processes: A Volume in Honour of Ron Doney's 80th Birthday
EditorsAndreas E. Kyprianou, Loïc Chaumon
Place of PublicationCham
Number of pages13
ISBN (electronic)9783030833091
ISBN (print)9783030833084
<mark>Original language</mark>English

Publication series

NameProgress in Probability
ISSN (Print)1050-6977


For a stochastic difference equation D n = A n D n−1 + B n which stabilises upon time we study tail distribution asymptotics for D n under the assumption that the distribution of log(1+|A1|+|B1|) is heavy-tailed, that is, all its positive exponential moments are infinite. The aim of the present paper is three-fold. Firstly, we identify the asymptotic behaviour not only of the stationary tail distribution but also of D n. Secondly, we solve the problem in the general setting when A takes both positive and negative values. Thirdly, we get rid of auxiliary conditions like finiteness of higher moments introduced in the literature before.