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August 2007 On invariant measures of stochastic recursions in a critical case
Dariusz Buraczewski
Ann. Appl. Probab. 17(4): 1245-1272 (August 2007). DOI: 10.1214/105051607000000140

Abstract

We consider an autoregressive model on ℝ defined by the recurrence equation Xn=AnXn−1+Bn, where {(Bn, An)} are i.i.d. random variables valued in ℝ×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 {Xn}. The aim of the paper is to investigate its behavior at infinity. We describe also stationary measures of two other stochastic recursions, including one arising in queuing theory.

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Dariusz Buraczewski. "On invariant measures of stochastic recursions in a critical case." Ann. Appl. Probab. 17 (4) 1245 - 1272, August 2007. https://doi.org/10.1214/105051607000000140

Information

Published: August 2007
First available in Project Euclid: 10 August 2007

zbMATH: 1151.60034
MathSciNet: MR2344306
Digital Object Identifier: 10.1214/105051607000000140

Subjects:
Primary: 60J10
Secondary: 60B15, 60G50

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.17 • No. 4 • August 2007
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