{"id":351,"date":"2017-11-17T17:13:11","date_gmt":"2017-11-17T17:13:11","guid":{"rendered":"http:\/\/pages.charlotte.edu\/probability-seminar\/?p=351"},"modified":"2017-11-17T17:13:11","modified_gmt":"2017-11-17T17:13:11","slug":"wed-nov-15-2017-at-345pm-in-fretwell-379-math-conference-room","status":"publish","type":"post","link":"https:\/\/pages.charlotte.edu\/probability-seminar\/blog\/2017\/11\/17\/wed-nov-15-2017-at-345pm-in-fretwell-379-math-conference-room\/","title":{"rendered":"Wed Nov 15, 2017 at 3:45PM in Fretwell 379 (Math Conference Room)"},"content":{"rendered":"<div class=\"entry-content\">\n<div class=\"entry-content\">\n<p><a href=\"http:\/\/math2.uncc.edu\/~imsonin\/\">Isaac Sonin<\/a> UNC Charlotte<\/p>\n<div class=\"entry-content\">\n<div>\n<p><i>Title: <\/i><span class=\"m_-7253915242511170420gmail-m_-2051454453909663613gmail-\"><span class=\"m_-7253915242511170420gmail-m_-2051454453909663613gmail-m_9055837596722250019gmail-\"><span class=\"m_-9042927162505197644gmail-m_-3211527944757434078gmail-m_-2051454453909663613gmail-\"><span class=\"m_-9042927162505197644gmail-m_-3211527944757434078gmail-m_-2051454453909663613gmail-m_9055837596722250019gmail-\">Insertion &#8211; A New Operation for Markov Chains and their Applications<\/span><\/span><br \/>\n<\/span><\/span><\/p>\n<p><em>Abstract:<\/em> It is well known that a Markov chain (MC), observed only when it is outside of a subset D, is again a MC, called the Censored MC, with a new transition matrix. This matrix can be obtained in |D| iterations, each requiring O(n^2) operations, when the states from D are &#8220;eliminated&#8221; one at a time. We show how to modify these iterations to allow for a state, previously eliminated, to be &#8220;reinserted&#8221; into the\u00a0 state space in one iteration. This modification sheds a new light on the relationship between an initial and censored MC, and introduces a new operation &#8211; &#8220;insertion&#8221; into the theory of MCs. We briefly describe the applications of these operations in different probability models, and even outside of Probability Theory.<\/p>\n<div class=\"yj6qo ajU\">\n<div id=\":zt\" class=\"ajR\" role=\"button\"><img decoding=\"async\" class=\"ajT\" src=\"https:\/\/ssl.gstatic.com\/ui\/v1\/icons\/mail\/images\/cleardot.gif\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Isaac Sonin UNC Charlotte Title: Insertion &#8211; A New Operation for Markov Chains and their Applications Abstract: It is well known that a Markov chain (MC), observed only when it is outside of a subset D, is again a MC, called the Censored MC, with a new transition matrix. This matrix can be obtained in [&hellip;]<\/p>\n","protected":false},"author":16,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-351","post","type-post","status-publish","format-standard","hentry","category-probability_seminar"],"_links":{"self":[{"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/posts\/351","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/users\/16"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/comments?post=351"}],"version-history":[{"count":1,"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/posts\/351\/revisions"}],"predecessor-version":[{"id":352,"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/posts\/351\/revisions\/352"}],"wp:attachment":[{"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/media?parent=351"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/categories?post=351"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/tags?post=351"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}