Yaglom limit via Holley inequality
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...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_01030752_v29_n2_p413_Ferrari |
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todo:paper_01030752_v29_n2_p413_Ferrari2023-10-03T14:57:29Z Yaglom limit via Holley inequality Ferrari, P.A. Rolla, L.T. Holley inequality Quasi-limiting distributions Quasi-stationary distributions Yaglom limit 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. © Brazilian Statistical Association, 2015. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_01030752_v29_n2_p413_Ferrari |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Holley inequality Quasi-limiting distributions Quasi-stationary distributions Yaglom limit |
| spellingShingle |
Holley inequality Quasi-limiting distributions Quasi-stationary distributions Yaglom limit Ferrari, P.A. Rolla, L.T. Yaglom limit via Holley inequality |
| topic_facet |
Holley inequality Quasi-limiting distributions Quasi-stationary distributions Yaglom limit |
| description |
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. © Brazilian Statistical Association, 2015. |
| format |
JOUR |
| author |
Ferrari, P.A. Rolla, L.T. |
| author_facet |
Ferrari, P.A. Rolla, L.T. |
| author_sort |
Ferrari, P.A. |
| title |
Yaglom limit via Holley inequality |
| title_short |
Yaglom limit via Holley inequality |
| title_full |
Yaglom limit via Holley inequality |
| title_fullStr |
Yaglom limit via Holley inequality |
| title_full_unstemmed |
Yaglom limit via Holley inequality |
| title_sort |
yaglom limit via holley inequality |
| url |
http://hdl.handle.net/20.500.12110/paper_01030752_v29_n2_p413_Ferrari |
| work_keys_str_mv |
AT ferraripa yaglomlimitviaholleyinequality AT rollalt yaglomlimitviaholleyinequality |
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1807315069890985984 |