{"id":6590,"date":"2018-09-07T12:50:31","date_gmt":"2018-09-07T11:50:31","guid":{"rendered":"http:\/\/smart--grid.net\/?page_id=6590"},"modified":"2022-12-03T23:01:58","modified_gmt":"2022-12-03T22:01:58","slug":"probabilite-dabsorption-dun-etat","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/es\/proceso-de-markov\/probabilidad-de-estado-absorcion\/","title":{"rendered":"Probabilidad de absorci\u00f3n de un estado"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"6590\" class=\"elementor elementor-6590\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3b20339 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3b20339\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-b06ded8\" data-id=\"b06ded8\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c046905 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"c046905\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/es\/proceso-de-markov\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Proceso de Markov<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-d8a1db1\" data-id=\"d8a1db1\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5c012d8 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"5c012d8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/es\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Pagina de inicio<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-c5e1c52\" data-id=\"c5e1c52\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c938b97 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"c938b97\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/fr.wikipedia.org\/wiki\/Cha%C3%AEne_de_Markov\" target=\"_blank\" rel=\"noopener\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Wiki<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-bb5dbb9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bb5dbb9\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4af1abf\" data-id=\"4af1abf\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-dc6b2a3 elementor-widget elementor-widget-progress\" data-id=\"dc6b2a3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"progress.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<span class=\"elementor-title\" id=\"elementor-progress-bar-dc6b2a3\">\n\t\t\t\tDificultad\t\t\t<\/span>\n\t\t\n\t\t<div aria-labelledby=\"elementor-progress-bar-dc6b2a3\" class=\"elementor-progress-wrapper\" role=\"progressbar\" aria-valuemin=\"0\" aria-valuemax=\"100\" aria-valuenow=\"50\" aria-valuetext=\"50% (Moyen)\">\n\t\t\t<div class=\"elementor-progress-bar\" data-max=\"50\">\n\t\t\t\t<span class=\"elementor-progress-text\">Promedio<\/span>\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-progress-percentage\">50%<\/span>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2295c3d2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2295c3d2\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-5f88cbea\" data-id=\"5f88cbea\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-10bc68dc elementor-widget elementor-widget-text-editor\" data-id=\"10bc68dc\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\n<h2>Absorci\u00f3n de un estado<\/h2>\n<p class=\"wp-block-paragraph\">A <a href=\"https:\/\/complex-systems-ai.com\/es\/proceso-de-markov\/cadenas-de-markov-en-tiempo-discreto\/\">cadena de markov<\/a> es absorbente (absorci\u00f3n de un estado) si y s\u00f3lo si: hay al menos un estado absorbente, de cualquier estado no absorbente se puede llegar a un estado absorbente. Para cualquier cadena de Markov absorbente y para cualquier estado inicial, la probabilidad de estar en un estado absorbente en el tiempo t tiende a 1 cuando t tiende a infinito.<\/p>\n\n<p class=\"wp-block-paragraph\">Cuando se trata de una cadena de Markov absorbente, generalmente nos interesan las dos preguntas siguientes:<\/p>\n\n<ul class=\"wp-block-list\">\n<li>\u00bfCu\u00e1nto tardar\u00e1 en promedio en llegar en estado absorbente, dado su estado inicial?<\/li>\n<li>Si hay varios estados absorbentes, \u00bfcu\u00e1l es la probabilidad de caer en un estado absorbente dado?<\/li>\n<\/ul>\n\n<p class=\"wp-block-paragraph\">Si una cadena de Markov es absorbente, colocaremos los estados absorbentes al principio; nosotros<br \/>entonces tendr\u00e1 una matriz de transici\u00f3n de la siguiente forma (I es una matriz unitaria y 0<br \/>una matriz de 0):<\/p>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone wp-image-6606\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba24.png\" alt=\"Absorci\u00f3n de un estado\" width=\"302\" height=\"177\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba24.png 302w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba24-300x176.png 300w\" sizes=\"(max-width: 302px) 100vw, 302px\" \/><\/figure>\n<\/div>\n\n<p class=\"wp-block-paragraph\">La matriz N = (IQ)<sup>-1<\/sup> se llama la matriz fundamental de la cadena absorbente. Considere la siguiente matriz estoc\u00e1stica:<\/p>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" class=\"alignnone wp-image-6607\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba25.png\" alt=\"Absorci\u00f3n de un estado\" width=\"208\" height=\"193\" title=\"\"><\/figure>\n<\/div>\n\n<p class=\"wp-block-paragraph\">Luego tenemos que calcular N:<\/p>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" class=\"alignnone wp-image-6608\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba26.png\" alt=\"Absorci\u00f3n de un estado\" width=\"549\" height=\"361\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba26.png 549w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba26-300x197.png 300w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/figure>\n<\/div>\n\n<div style=\"padding: 5px; background-color: #ffdcd3; border: 2px solid #ff7964; -moz-border-radius: 9px; -khtml-border-radius: 9px; -webkit-border-radius: 9px; border-radius: 9px;\">El n\u00famero medio e<sub>ij<\/sub> de cambios al estado j (no absorbente) antes de la absorci\u00f3n cuando se parte del estado i (no absorbente) viene dado por e<sub>ij<\/sub> = (N)<sub>ij<\/sub>.<br \/>El n\u00famero medio de pasos antes de la absorci\u00f3n sabiendo que partimos del estado i (no<br \/>absorbente) es la suma de los t\u00e9rminos de la i-\u00e9sima fila de N.<\/div>\n\n<p class=\"wp-block-paragraph\">En el ejemplo anterior, el n\u00famero medio de pasos antes de la absorci\u00f3n se toma de la primera l\u00ednea, comenzando desde el estado 1: 320\/37 + 160\/37 + 100\/37 = 15,67.<\/p>\n\n<div style=\"padding: 5px; background-color: #ffdcd3; border: 2px solid #ff7964; -moz-border-radius: 9px; -khtml-border-radius: 9px; -webkit-border-radius: 9px; border-radius: 9px;\">En una cadena de Markov absorbente con P colocado debajo <a href=\"https:\/\/complex-systems-ai.com\/es\/programacion-lineal\/lp-forma-canonica-y-forma-estandar-2\/\">forma can\u00f3nica<\/a>, el t\u00e9rmino b<sub>ij<\/sub> de la matriz B = NR es la probabilidad de absorci\u00f3n por el estado absorbente j sabiendo que partimos del estado i.<\/div>\n\n<p class=\"wp-block-paragraph\">En el mismo ejemplo:<\/p>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-6609\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba27.png\" alt=\"Absorci\u00f3n de un estado\" width=\"528\" height=\"169\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba27.png 528w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba27-300x96.png 300w\" sizes=\"(max-width: 528px) 100vw, 528px\" \/><\/figure>\n<\/div>\n\n<p class=\"wp-block-paragraph\">La probabilidad de ser absorbido por el estado absorbente \u00fanico es 1, sea cual sea el estado inicial.<\/p>\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Equations-lineaires\"><\/span>Ecuaciones lineales<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"wp-block-paragraph\">Desde el punto de vista de una ecuaci\u00f3n lineal, el vector de probabilidades de absorci\u00f3n es la soluci\u00f3n positiva m\u00e1s peque\u00f1a del sistema:<\/p>\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-6613\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba28.png\" alt=\"Absorci\u00f3n de un estado\" width=\"534\" height=\"79\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba28.png 534w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba28-300x44.png 300w\" sizes=\"(max-width: 534px) 100vw, 534px\" \/><\/figure>\n\n<p class=\"wp-block-paragraph\">El vector de <a href=\"https:\/\/complex-systems-ai.com\/es\/proceso-de-markov\/probabilidad-de-un-estado\/\">tiempo medio para llegar<\/a> es la soluci\u00f3n positiva m\u00e1s peque\u00f1a del sistema:<\/p>\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-6614\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba29.png\" alt=\"Absorci\u00f3n de un estado\" width=\"782\" height=\"83\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba29.png 782w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba29-300x32.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2018\/09\/proba29-768x82.png 768w\" sizes=\"(max-width: 782px) 100vw, 782px\" \/><\/figure>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Proceso de Markov Wiki Inicio Dificultad Media 50% Absorci\u00f3n de un estado Una cadena de Markov es absorbente (absorbe un estado) si y solo si... <\/p>","protected":false},"author":1,"featured_media":0,"parent":5007,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-6590","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/6590","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/comments?post=6590"}],"version-history":[{"count":7,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/6590\/revisions"}],"predecessor-version":[{"id":18660,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/6590\/revisions\/18660"}],"up":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/5007"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/media?parent=6590"}],"curies":[{"name":"gracias","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}