{"id":9332,"date":"2023-06-20T14:19:34","date_gmt":"2023-06-20T12:19:34","guid":{"rendered":"https:\/\/www.dm.unipi.it\/?post_type=unipievents&#038;p=9332"},"modified":"2023-06-28T10:04:04","modified_gmt":"2023-06-28T08:04:04","slug":"large-deviations-for-empirical-measures-of-self-interacting-markov-chains","status":"publish","type":"unipievents","link":"https:\/\/www.dm.unipi.it\/en\/eventi\/large-deviations-for-empirical-measures-of-self-interacting-markov-chains\/","title":{"rendered":"Large Deviations for Empirical Measures of Self-Interacting  Markov Chains &ndash; Pavlos Zoubouloglou (University of North Carolina)"},"content":{"rendered":"\n<p>Let $\\Delta^o$ be a finite set and, for each probability measure $m$ on $\\Delta^o$, let $G(m)$ be a transition kernel on $\\Delta^o$. Consider the sequence $\\{X_n\\}$ of $\\Delta^o$-valued random variables such that, and given $X_0,\\ldots,X_n$, the conditional distribution of $X_{n+1}$ is $G(L^{n+1})(X_n,\\cdot)$, where $L^{n+1}=\\frac{1}{n+1}\\sum_{i=0}^{n}\\delta_{X_i}$. Under conditions on $G$ we establish a large deviation principle for the sequence $\\{L^n\\}$. As one application of this result we obtain large deviation asymptotics for the Aldous-Flannery-Palacios (1988) approximation scheme for quasi-stationary distributions of finite state Markov chains. The conditions on $G$ cover other models as well, including certain models with edge or vertex reinforcement.<\/p>\n\n\n\n<p><strong>Arxiv link:<\/strong>&nbsp;<a href=\"https:\/\/arxiv.org\/abs\/2304.01384\">https:\/\/arxiv.org\/abs\/2304.01384<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let $\\Delta^o$ be a finite set and, for each probability measure $m$ on $\\Delta^o$, let $G(m)$ be a transition kernel&hellip;<\/p>\n<p><a class=\"btn btn-dark btn-sm unipi-read-more-link\" href=\"https:\/\/www.dm.unipi.it\/en\/eventi\/large-deviations-for-empirical-measures-of-self-interacting-markov-chains\/\">Read More&#8230;<\/a><\/p>\n","protected":false},"author":15,"featured_media":0,"template":"","tags":[],"unipievents_taxonomy":[],"class_list":["post-9332","unipievents","type-unipievents","status-publish","hentry"],"acf":[],"unipievents_startdate":1688047200,"unipievents_enddate":1688050800,"unipievents_place":"Aula Seminari","unipievents_externalid":0,"jetpack_sharing_enabled":true,"publishpress_future_workflow_manual_trigger":{"enabledWorkflows":[]},"_links":{"self":[{"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents\/9332","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents"}],"about":[{"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/types\/unipievents"}],"author":[{"embeddable":true,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":3,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents\/9332\/revisions"}],"predecessor-version":[{"id":9370,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents\/9332\/revisions\/9370"}],"wp:attachment":[{"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/media?parent=9332"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/tags?post=9332"},{"taxonomy":"unipievents_taxonomy","embeddable":true,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents_taxonomy?post=9332"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}