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

Gerardo Barrera, Shuo Liu

Research output: Contribution to journalArticlepeer-review

Abstract

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.
Original languageEnglish
JournalBrazilian Journal of Probability and Statistics
Volume35
Issue number2
Pages (from-to)224-241
Number of pages18
ISSN0103-0752
DOIs
Publication statusPublished - May 2021
Externally publishedYes
MoE publication typeA1 Journal article-refereed

Fields of Science

  • 111 Mathematics
  • Linear recurrences
  • 112 Statistics and probability
  • Cut-off phenomenon
  • Gaussian distribution
  • Total variation distance
  • linear recurrences
  • Gaussian distribution
  • total variation dis-tance
  • &amp
  • nbsp
  • Cut-off phenomenon

Cite this