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

Fraser Daly

doi:10.1016/j.spl.2023.109993

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

Fraser Daly

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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 language	English
Article number	109993
Journal	Statistics and Probability Letters
Volume	206
Early online date	23 Nov 2023
DOIs	https://doi.org/10.1016/j.spl.2023.109993
Publication status	Published - 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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AB - 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.

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KW - Poisson's equation

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KW - Stochastic monotonicity

KW - Total variation distance

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

Abstract

Keywords

ASJC Scopus subject areas

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