Yaglom limit via Holley inequality.

LEONARDO ROLLA; PABLO A. FERRARI

BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS

Assoc. Brasileira Estatíst.

Lugar: Sao Paulo; Año: 2015 vol. 29 p. 413 - 423

0103-0752

Let S be a countable set provided with a partial order and a minimal element. Consider a Markov chain on S∪{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.