@article{DYSZEWSKI2016392,
title = {Iterated random functions and slowly varying tails},
journal = {Stochastic Processes and their Applications},
volume = {126},
number = {2},
pages = {392-413},
year = {2016},
issn = {0304-4149},
doi = {https://doi.org/10.1016/j.spa.2015.09.005},
url = {https://www.sciencedirect.com/science/article/pii/S0304414915002239},
author = {Piotr Dyszewski},
keywords = {Stochastic recursions, Random difference equation, Stationary distribution, Subexponential distributions},
abstract = {Consider a sequence of i.i.d. random Lipschitz functions {Ψn}n≥0. Using this sequence we can define a Markov chain via the recursive formula Rn+1=Ψn+1(Rn). It is a well known fact that under some mild moment assumptions this Markov chain has a unique stationary distribution. We are interested in the tail behaviour of this distribution in the case when Ψ0(t)≈A0t+B0. We will show that under subexponential assumptions on the random variable log+(A0∨B0) the tail asymptotic in question can be described using the integrated tail function of log+(A0∨B0). In particular we will obtain new results for the random difference equation Rn+1=An+1Rn+Bn+1.}
}