On Stein’s method for stochastically monotone single-birth chains

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Abstract

We discuss Stein's method for approximation by the stationary distribution of a single-birth Markov chain, in conjunction with stochastic monotonicity and similar assumptions. We use bounds on the increments of the solution of Poisson's equation for such a process. Applications include rates of convergence to stationarity, and bounding the total variation distance between the stationary distributions of two Markov chains in the case where one transition matrix dominates the other.
Original languageEnglish
Article number109993
JournalStatistics and Probability Letters
Volume206
Early online date23 Nov 2023
DOIs
Publication statusPublished - Mar 2024

Keywords

  • Markov chain
  • Poisson's equation
  • Stein's method
  • Stochastic monotonicity
  • Total variation distance

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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