TY - CHAP

T1 - Slowly varying asymptotics for signed stochastic difference equations

AU - Korshunov, Dmitry

PY - 2021/12/1

Y1 - 2021/12/1

N2 - 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.

AB - 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.

U2 - 10.1007/978-3-030-83309-1_14

DO - 10.1007/978-3-030-83309-1_14

M3 - Chapter (peer-reviewed)

SN - 9783030833084

T3 - Progress in Probability

SP - 245

EP - 257

BT - A Lifetime of Excursions Through Random Walks and Lévy Processes

A2 - Kyprianou, Andreas E.

A2 - Chaumon, Loïc

PB - Birkhauser

CY - Cham

ER -