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May 2015 Yaglom limit via Holley inequality
Pablo A. Ferrari, Leonardo T. Rolla
Braz. J. Probab. Stat. 29(2): 413-426 (May 2015). DOI: 10.1214/14-BJPS269


Let ${S}$ be a countable set provided with a partial order and a minimal element. Consider a Markov chain on $S\cup\{0\}$ absorbed at $0$ with a quasi-stationary distribution. We use Holley inequality to obtain sufficient conditions under which the following hold. The trajectory of the chain starting from the minimal state is stochastically dominated by the trajectory of the chain starting from any probability on ${S}$, when both are conditioned to nonabsorption until a certain time. Moreover, the Yaglom limit corresponding to this deterministic initial condition is the unique minimal quasi-stationary distribution in the sense of stochastic order. As an application, we provide new proofs to classical results in the field.


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Pablo A. Ferrari. Leonardo T. Rolla. "Yaglom limit via Holley inequality." Braz. J. Probab. Stat. 29 (2) 413 - 426, May 2015.


Published: May 2015
First available in Project Euclid: 15 April 2015

zbMATH: 1321.60142
MathSciNet: MR3336873
Digital Object Identifier: 10.1214/14-BJPS269

Keywords: Holley inequality , quasi-limiting distributions , Quasi-stationary distributions , Yaglom limit

Rights: Copyright © 2015 Brazilian Statistical Association


Vol.29 • No. 2 • May 2015
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