We study solutions to the stochastic fixed point equation \\(X\\stackrel{d}{=}AX+B\\) where the coefficients \\(A\\) and \\(B\\) are nonnegative random variables. We introduce the “local dependence measure” (LDM) and its Legendre-type transform to analyze the left tail behavior of the distribution of \\(X\\). We discuss the relationship of LDM with earlier results on the stochastic fixed point equation and we apply LDM to prove a theorem on a Fleming-Viot-type process.<\/p>\n","protected":false},"excerpt":{"rendered":"
We study solutions to the stochastic fixed point equation where the coefficients and are nonnegative random variables. We introduce the “local dependence measure” (LDM) and its Legendre-type transform to analyze the left tail behavior of the distribution of . We discuss the relationship of LDM with earlier results on the stochastic fixed point equation and […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":[{"type":"text","value":"Krzysztof Burdzy","user_id":0},{"type":"text","value":"Bartosz Ko\u0142odziejek","user_id":0},{"type":"user_nicename","value":"Tvrtko Tadi\u0107","user_id":"43653"}],"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"The Annals of Applied Probability","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"","msr_doi":"10.1214\/21-aap1749","msr_arxiv_id":"","msr_mag_id":"","msr_other_authors":"","msr_other_contributors":"","msr_speaker":"","msr_award":"","msr_affiliation":"","msr_institution":"","msr_host":"","msr_version":"","msr_duration":"","msr_release_tracker_id":"","msr_highlight_type":"","msr_date_display_format":"","msr_main_download_label":"","msr_external_link_label":"","msr_doi_label":"","msr_published_date":"2022-08-01","msr_startdate":"","msr_presentation_date":"","msr_highlight_text":"","msr_notes":"","msr_longbiography":"","msr_publicationurl":"","msr_external_url":"","msr_secondary_video_url":"","msr_conference_url":"","msr_journal_url":"","msr_year":2022,"msr_month":8,"msr_day":1,"msr_microsoftintellectualproperty":true,"msr_pub_id":"","msr_publication_uploader":[{"type":"doi","viewUrl":"false","id":false,"title":"https:\/\/doi.org\/10.1214\/21-aap1749","label_id":243106,"label":0},{"type":"url","viewUrl":"false","id":false,"title":"https:\/\/arxiv.org\/abs\/2004.01850","label_id":243109,"label":0},{"type":"url","viewUrl":"false","id":false,"title":"http:\/\/arxiv.org\/pdf\/2004.01850","label_id":243109,"label":0}],"msr_related_uploader":[],"msr_original_fields_of_study":["mathematics"],"msr_s2_paper_id":"","msr_s2_pdf_url":"","msr_citation_count_updated":"","msr_citation_count":0,"msr_influential_citations":0,"msr_reference_count":0,"msr_s2_open_access":false,"msr_s2_author_ids":[],"msr_pub_ids":[],"msr_hide_image_in_river":null,"footnotes":""},"msr-research-highlight":[],"research-area":[13546],"msr-publication-type":[193715],"msr-publisher":[],"msr-publication-cta":[],"msr-focus-area":[],"msr-locale":[268875],"msr-post-option":[269148,269142],"msr-field-of-study":[246907],"msr-conference":[],"msr-journal":[269169],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-1097772","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-computational-sciences-mathematics","msr-locale-en_us","msr-post-option-approved-for-river","msr-post-option-include-in-river","msr-field-of-study-mathematics"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2022-08-01","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"","msr_chapter":"","msr_isbn":"","msr_journal":"The Annals of Applied Probability","msr_volume":"","msr_number":"","msr_editors":"","msr_series":"","msr_issue":"","msr_organization":"","msr_how_published":"","msr_notes":"","msr_highlight_text":"","msr_release_tracker_id":"","msr_original_fields_of_study":"","msr_download_urls":"","msr_external_url":"","msr_secondary_video_url":"","msr_longbiography":"","msr_microsoftintellectualproperty":1,"msr_main_download":"","msr_publicationurl":"","msr_doi":"10.1214\/21-aap1749","msr_publication_uploader":[{"type":"doi","viewUrl":"false","id":"false","title":"https:\/\/doi.org\/10.1214\/21-aap1749","label_id":"243106","label":0},{"type":"url","viewUrl":"false","id":"false","title":"https:\/\/arxiv.org\/abs\/2004.01850","label_id":"243109","label":0},{"type":"url","viewUrl":"false","id":"false","title":"http:\/\/arxiv.org\/pdf\/2004.01850","label_id":"243109","label":0}],"msr_related_uploader":[],"msr_citation_count":0,"msr_citation_count_updated":"","msr_s2_paper_id":"","msr_influential_citations":0,"msr_reference_count":0,"msr_arxiv_id":"","msr_s2_author_ids":[],"msr_s2_open_access":false,"msr_s2_pdf_url":null,"msr_attachments":[],"msr-author-ordering":[{"type":"text","value":"Krzysztof Burdzy","user_id":0,"rest_url":false},{"type":"text","value":"Bartosz Ko\u0142odziejek","user_id":0,"rest_url":false},{"type":"user_nicename","value":"Tvrtko Tadi\u0107","user_id":43653,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Tvrtko Tadi\u0107"}],"msr_impact_theme":[],"msr_research_lab":[],"msr_event":[],"msr_group":[],"msr_project":[],"publication":[],"video":[],"msr-tool":[],"msr_publication_type":"article","related_content":[],"_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/1097772","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-research-item"}],"version-history":[{"count":1,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/1097772\/revisions"}],"predecessor-version":[{"id":1097775,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/1097772\/revisions\/1097775"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=1097772"}],"wp:term":[{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=1097772"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=1097772"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=1097772"},{"taxonomy":"msr-publisher","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publisher?post=1097772"},{"taxonomy":"msr-publication-cta","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-cta?post=1097772"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=1097772"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=1097772"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=1097772"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=1097772"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=1097772"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=1097772"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=1097772"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=1097772"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}