A Phase Transition for Large Values of Bifurcating Autoregressive Models

We describe the asymptotic behavior of the number Z n [ a n , ∞ ) of individuals with a large value in a stable bifurcating autoregressive process, where a n → ∞ . The study of the associated first moment is equivalent to the annealed large deviation problem of an autoregressive process in a random...

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Veröffentlicht in:	Journal of theoretical probability 2021-12, Vol.34 (4), p.2081-2116
Hauptverfasser:	Bansaye, Vincent, Bitseki Penda, S. Valère
Format:	Artikel
Sprache:	eng
Schlagworte:	Asymptotic properties Autoregressive models Autoregressive processes Bifurcations Deviation Mathematics Mathematics and Statistics Phase transitions Probability Probability Theory and Stochastic Processes Statistics
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