An order-theoretic mixing condition for monotone Markov chains

Takashi Kamihigashi; John Stachurski

doi:10.1016/j.spl.2011.09.024

An order-theoretic mixing condition for monotone Markov chains

Takashi Kamihigashi^*, John Stachurski

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

We discuss the stability of discrete-time Markov chains satisfying monotonicity and an order-theoretic mixing condition that can be seen as an alternative to irreducibility. A chain satisfying these conditions has at most one stationary distribution. Moreover, if there is a stationary distribution, then the chain is stable in an order-theoretic sense.

Original language	English
Pages (from-to)	262-267
Number of pages	6
Journal	Statistics and Probability Letters
Volume	82
Issue number	2
DOIs	https://doi.org/10.1016/j.spl.2011.09.024
Publication status	Published - Feb 2012

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10.1016/j.spl.2011.09.024

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title = "An order-theoretic mixing condition for monotone Markov chains",

abstract = "We discuss the stability of discrete-time Markov chains satisfying monotonicity and an order-theoretic mixing condition that can be seen as an alternative to irreducibility. A chain satisfying these conditions has at most one stationary distribution. Moreover, if there is a stationary distribution, then the chain is stable in an order-theoretic sense.",

keywords = "Coupling, Irreducibility, Markov chains, Mixing, Monotonicity",

author = "Takashi Kamihigashi and John Stachurski",

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T1 - An order-theoretic mixing condition for monotone Markov chains

AU - Kamihigashi, Takashi

AU - Stachurski, John

PY - 2012/2

Y1 - 2012/2

N2 - We discuss the stability of discrete-time Markov chains satisfying monotonicity and an order-theoretic mixing condition that can be seen as an alternative to irreducibility. A chain satisfying these conditions has at most one stationary distribution. Moreover, if there is a stationary distribution, then the chain is stable in an order-theoretic sense.

AB - We discuss the stability of discrete-time Markov chains satisfying monotonicity and an order-theoretic mixing condition that can be seen as an alternative to irreducibility. A chain satisfying these conditions has at most one stationary distribution. Moreover, if there is a stationary distribution, then the chain is stable in an order-theoretic sense.

KW - Coupling

KW - Irreducibility

KW - Markov chains

KW - Mixing

KW - Monotonicity

UR - https://www.scopus.com/pages/publications/80855130315

U2 - 10.1016/j.spl.2011.09.024

DO - 10.1016/j.spl.2011.09.024

M3 - Article

SN - 0167-7152

VL - 82

SP - 262

EP - 267

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 2

ER -

An order-theoretic mixing condition for monotone Markov chains

Abstract

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