# On invariant measures of stochastic recursions in a critical case

@article{Buraczewski2007OnIM,
title={On invariant measures of stochastic recursions in a critical case},
author={Dariusz Buraczewski},
journal={Annals of Applied Probability},
year={2007},
volume={17},
pages={1245-1272}
}
• D. Buraczewski
• Published 1 August 2007
• Mathematics
• Annals of Applied Probability
We consider an autoregressive model on $\mathbb{R}$ defined by the recurrence equation $X_n=A_nX_{n-1}+B_n$, where $\{(B_n,A_n)\}$ are i.i.d. random variables valued in $\mathbb{R}\times\mathbb{R}^+$ and $\mathbb {E}[\log A_1]=0$ (critical case). It was proved by Babillot, Bougerol and Elie that there exists a unique invariant Radon measure of the process $\{X_n\}$. The aim of the paper is to investigate its behavior at infinity. We describe also stationary measures of two other stochastic…
Tail homogeneity of invariant measures of multidimensional stochastic recursions in a critical case
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