Korshunov, Dmitry
(2021)
*Slowly varying asymptotics for signed stochastic difference equations.*
In:
A Lifetime of Excursions Through Random Walks and Lévy Processes : A Volume in Honour of Ron Doney's 80th Birthday.
Progress in Probability
.
Birkhauser, Cham, pp. 245-257.
ISBN 9783030833084

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## Abstract

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.