2016
DOI: 10.1214/15-aihp668
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Spectral gap properties for linear random walks and Pareto’s asymptotics for affine stochastic recursions

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Cited by 50 publications
(117 citation statements)
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“…Basic aspects of these special processes continue to hold in the general case of X x n , and give a heuristic guide for the study of the affine random walk X x n . On the other hand, independently of any density condition for µ, the conjunction of these two different processes give rise to new properties, in particular spectral gap properties for P (Cf [5,21]) and homogeneity at infinity for the P -stationary measure(Cf [6,17,22]). …”
Section: Introduction and Main Resultsmentioning
confidence: 99%
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“…Basic aspects of these special processes continue to hold in the general case of X x n , and give a heuristic guide for the study of the affine random walk X x n . On the other hand, independently of any density condition for µ, the conjunction of these two different processes give rise to new properties, in particular spectral gap properties for P (Cf [5,21]) and homogeneity at infinity for the P -stationary measure(Cf [6,17,22]). …”
Section: Introduction and Main Resultsmentioning
confidence: 99%
“…A remarkable property of η is its "homogeneity at infinity", a property which was first observed in [31] for the tails of η, extended to the general case in [34] and further developed in [1,6,13], under special conditions. See [17] for a survey of [34] as well for a precise description of the homogeneity property of η, proved in a special case in [6] and in a generic case in [22].…”
Section: Introduction and Main Resultsmentioning
confidence: 99%
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