A switch convergence for a small perturbation of a linear recurrence equation

Gerardo Barrera, Shuo Liu

Forskningsoutput: TidskriftsbidragArtikelVetenskapligPeer review

Sammanfattning

In this article we study a small random perturbation of a linear recurrence
equation. If all the roots of its corresponding characteristic equation
have modulus strictly less than one, the random linear recurrence goes exponentially
fast to its limiting distribution in the total variation distance as time
increases. By assuming that all the roots of its corresponding characteristic
equation have modulus strictly less than one and rather mild conditions, we
prove that this convergence happens as a switch-type, i.e., there is a sharp
transition in the convergence to its limiting distribution. This fact is known as
a cut-off phenomenon in the context of stochastic processes.
Originalspråkengelska
TidskriftBrazilian Journal of Probability and Statistics
Volym35
Utgåva2
Sidor (från-till)224-241
Antal sidor18
ISSN0103-0752
DOI
StatusPublicerad - maj 2021
Externt publiceradJa
MoE-publikationstypA1 Tidskriftsartikel-refererad

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  • 111 Matematik
  • 112 Statistik

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