{
  "http://en.wikipedia.org/wiki/Natural_filtration" : { "http://xmlns.com/foaf/0.1/primaryTopic" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/Natural_filtration" } ] } ,
  "http://dbpedia.org/resource/Brownian_model_of_financial_markets" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/Natural_filtration" } ] } ,
  "http://dbpedia.org/resource/It\u00F4_isometry" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/Natural_filtration" } ] } ,
  "http://dbpedia.org/resource/Law_of_total_variance" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/Natural_filtration" } ] } ,
  "http://dbpedia.org/resource/Markov_property" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/Natural_filtration" } ] } ,
  "http://dbpedia.org/resource/Adapted_process" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/Natural_filtration" } ] } ,
  "http://dbpedia.org/resource/Catalog_of_articles_in_probability_theory" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/Natural_filtration" } ] } ,
  "http://dbpedia.org/resource/Short-rate_model" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/Natural_filtration" } ] } ,
  "http://dbpedia.org/resource/Brownian_motion" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/Natural_filtration" } ] } ,
  "http://dbpedia.org/resource/It\u00F4_diffusion" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/Natural_filtration" } ] } ,
  "http://dbpedia.org/resource/Filtration_(mathematics)" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/Natural_filtration" } ] } ,
  "http://dbpedia.org/resource/Natural_filtration" : { "http://www.w3.org/1999/02/22-rdf-syntax-ns#type" : [ { "type" : "uri", "value" : "http://dbpedia.org/class/yago/PsychologicalFeature100023100" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/class/yago/StochasticProcess113561896" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/class/yago/Cognition100023271" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/class/yago/Concept105835747" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/class/yago/Model105890249" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/class/yago/Hypothesis105888929" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/class/yago/Idea105833840" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/class/yago/Abstraction100002137" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/class/yago/Content105809192" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/class/yago/WikicatStochasticProcesses" } ] ,
    "http://www.w3.org/2000/01/rdf-schema#label" : [ { "type" : "literal", "value" : "Natural filtration" , "lang" : "en" } ] ,
    "http://www.w3.org/2000/01/rdf-schema#comment" : [ { "type" : "literal", "value" : "In the theory of stochastic processes in mathematics and statistics, the generated filtration or natural filtration associated to a stochastic process is a filtration associated to the process which records its \"past behaviour\" at each time. It is in a sense the simplest filtration available for studying the given process: all information concerning the process, and only that information, is available in the natural filtration. i.e., the smallest \u03C3-algebra on \u03A9 that contains all pre-images of \u03A3-measurable subsets of S for \"times\" j up to i." , "lang" : "en" } ] ,
    "http://purl.org/dc/terms/subject" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/Category:Stochastic_processes" } ] ,
    "http://dbpedia.org/ontology/abstract" : [ { "type" : "literal", "value" : "In the theory of stochastic processes in mathematics and statistics, the generated filtration or natural filtration associated to a stochastic process is a filtration associated to the process which records its \"past behaviour\" at each time. It is in a sense the simplest filtration available for studying the given process: all information concerning the process, and only that information, is available in the natural filtration. More formally, let (\u03A9, F, P) be a probability space; let (I, \u2264) be a totally ordered index set; let (S, \u03A3) be a measurable space; let X : I \u00D7 \u03A9 \u2192 S be a stochastic process. Then the natural filtration of F with respect to X is defined to be the filtration F\u2022X = (FiX)i\u2208I given by i.e., the smallest \u03C3-algebra on \u03A9 that contains all pre-images of \u03A3-measurable subsets of S for \"times\" j up to i. In many examples, the index set I is the natural numbers N (possibly including 0) or an interval [0, T] or [0, +\u221E); the state space S is often the real line R or Euclidean space Rn. Any stochastic process X is an adapted process with respect to its natural filtration." , "lang" : "en" } ] ,
    "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/Category:Stochastic_processes" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Stochastic_processes" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Adapted_process" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Index_set" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Interval_(mathematics)" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Filtration_(probability_theory)" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Measurable_space" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Statistics" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Probability_space" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Filtration_(mathematics)" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Natural_numbers" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Mathematics" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Sigma_algebra" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Total_order" } ] ,
    "http://dbpedia.org/property/wikiPageUsesTemplate" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/Template:Citation" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Template:Reflist" } ] ,
    "http://dbpedia.org/ontology/wikiPageRevisionID" : [ { "type" : "literal", "value" : 868556916 , "datatype" : "http://www.w3.org/2001/XMLSchema#integer" } ] ,
    "http://dbpedia.org/ontology/wikiPageLength" : [ { "type" : "literal", "value" : "1869" , "datatype" : "http://www.w3.org/2001/XMLSchema#nonNegativeInteger" } ] ,
    "http://dbpedia.org/ontology/wikiPageID" : [ { "type" : "literal", "value" : 5864648 , "datatype" : "http://www.w3.org/2001/XMLSchema#integer" } ] ,
    "http://www.w3.org/2002/07/owl#sameAs" : [ { "type" : "uri", "value" : "http://www.wikidata.org/entity/Q6980678" } ,
      { "type" : "uri", "value" : "http://yago-knowledge.org/resource/Natural_filtration" } ,
      { "type" : "uri", "value" : "http://rdf.freebase.com/ns/m.0f9rdv" } ,
      { "type" : "uri", "value" : "http://dbpedia.org/resource/Natural_filtration" } ,
      { "type" : "uri", "value" : "https://global.dbpedia.org/id/4sMo3" } ] ,
    "http://www.w3.org/ns/prov#wasDerivedFrom" : [ { "type" : "uri", "value" : "http://en.wikipedia.org/wiki/Natural_filtration?oldid=868556916&ns=0" } ] ,
    "http://xmlns.com/foaf/0.1/isPrimaryTopicOf" : [ { "type" : "uri", "value" : "http://en.wikipedia.org/wiki/Natural_filtration" } ] } ,
  "http://dbpedia.org/resource/Filtration_(probability_theory)" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/Natural_filtration" } ] } ,
  "http://dbpedia.org/resource/Generated_filtration" : { "http://dbpedia.org/ontology/wikiPageWikiLink" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/Natural_filtration" } ] ,
    "http://dbpedia.org/ontology/wikiPageRedirects" : [ { "type" : "uri", "value" : "http://dbpedia.org/resource/Natural_filtration" } ] }
}
  <script>parent.window.postMessage('ixistenz.url:http://dbpedia.org/data/Natural_filtration.json', '*'); </script> <div id='browserdiffcontainer' style='position: fixed; right: 10px; top: 10vh; min-width: 60px;  border: 1px solid white; background: rgb(251, 189, 0);; opacity: 0.9; font-family: helvetica, arial, sans serif;  font-size: 12px; z-index: 20001; padding-bottom: 20px;'><div onclick="toggle('browserdiffcontainerlist'); return false;" style='background: rgb(151, 89, 0);; color: white; '><strong>&nbsp; <span class='glyphicon glyphicon-minus'></span> NODES</strong></div><div id='browserdiffcontainerlist' style='padding-left: 10px; padding-right: 5px; max-height: 50vh; overflow: auto; '><div><a href='#diffid884' style='color: white;' onClick="parent.window.postMessage('ixistenz.opendiff:884', '*');; return false;" style='text-decoration: none; '>Idea </a> <a style='color: white;' href='#diffid884'><sup>2</sup></a></div><div><a href='#diffid119' style='color: white;' onClick="parent.window.postMessage('ixistenz.opendiff:119', '*');; return false;" style='text-decoration: none; '>idea </a> <a style='color: white;' href='#diffid119'><sup>2</sup></a></div></div></div>
<script>
function toggle( divname ) {
  var x = document.getElementById( divname );
  if (x.style.display === 'none') {
    x.style.display = 'block';
  } else {
    x.style.display = 'none';
  }
} </script>