{"id":237196,"date":"2026-05-14T22:30:17","date_gmt":"2026-05-15T03:30:17","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2026\/05\/law-of-the-iterated-logarithm"},"modified":"2026-05-14T22:30:17","modified_gmt":"2026-05-15T03:30:17","slug":"law-of-the-iterated-logarithm","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2026\/05\/law-of-the-iterated-logarithm","title":{"rendered":"Law of the iterated logarithm"},"content":{"rendered":"<p><a class=\"aligncenter blog-photo\" href=\"https:\/\/lifeboat.com\/blog.images\/law-of-the-iterated-logarithm2.gif\"><\/a><\/p>\n<p>Where \u201clog\u201d is the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Natural_logarithm\" title=\"Natural logarithm\">natural logarithm<\/a>, \u201clim sup\u201d denotes the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Limit_superior\" title=\"Limit superior\">limit superior<\/a>, and \u201ca.s.\u201d stands for \u201c<a href=\"https:\/\/en.wikipedia.org\/wiki\/Almost_surely\" title=\"Almost surely\">almost surely<\/a>\u201d.<sup id=\u201d cite_ref-3\u201d class=\u201d reference\u201d><a href=\"https:\/\/en.wikipedia.org\/wiki\/Law_of_the_iterated_logarithm?utm_source#cite_note-3\"> [ 3 ]<\/a> <\/sup><sup id=\u201d cite_ref-4\u201d class=\u201d reference\u201d><a href=\"https:\/\/en.wikipedia.org\/wiki\/Law_of_the_iterated_logarithm?utm_source#cite_note-4\"> [ 4 ]<\/a><\/sup><\/p>\n<p>Another statement given by <a href=\"https:\/\/en.wikipedia.org\/wiki\/Andrey_Kolmogorov\" title=\"Andrey Kolmogorov\">A. N. Kolmogorov<\/a> in 1929<sup id= cite_ref-Kolmogorov1929_2-1 class= reference><a href=\"https:\/\/en.wikipedia.org\/wiki\/Law_of_the_iterated_logarithm?utm_source#cite_note-Kolmogorov1929-2\"> [ 2 ]<\/a> <\/sup> is as follows.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Where \u201clog\u201d is the natural logarithm, \u201clim sup\u201d denotes the limit superior, and \u201ca.s.\u201d stands for \u201calmost surely\u201d. [ 3 ] [ 4 ] Another statement given by A. N. Kolmogorov in 1929 [ 2 ] is as follows.<\/p>\n","protected":false},"author":709,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[20],"tags":[],"class_list":["post-237196","post","type-post","status-publish","format-standard","hentry","category-futurism"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/237196","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/709"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=237196"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/237196\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=237196"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=237196"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=237196"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}