## Yaglom limit via Holley inequality.(English)Zbl 1321.60142

Summary: 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 the Holley inequality to obtain sufficient conditions under which the following holds: 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.

### MSC:

 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) 60E15 Inequalities; stochastic orderings
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### References:

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