{"id":234,"date":"2023-01-13T13:55:30","date_gmt":"2023-01-13T13:55:30","guid":{"rendered":"https:\/\/do.csc.knu.ua\/?p=234"},"modified":"2025-12-22T10:02:49","modified_gmt":"2025-12-22T10:02:49","slug":"poisson-hulls","status":"publish","type":"post","link":"https:\/\/do.csc.knu.ua\/?p=234","title":{"rendered":"Poisson Hulls"},"content":{"rendered":"<div class=\"contentpaneopen\">\n<p class=\"contentheading\"><span style=\"font-size: 1.94em;\">28 \u043a\u0432\u0456\u0442\u043d\u044f 2021 \u0440\u043e\u043a\u0443 \u043e 14 \u0433\u043e\u0434 15 \u0445\u0432<\/span><\/p>\n<div class=\"article-content\">\n<p>We consider a hull operator on Poisson point processes, the easiest example being the convex hull of the support. Assuming that theintensity measure of the process is known on the set generated by the hull operator, we discuss estimation of the expected symmetricstatistics built on the Poisson process. The results are based on a stopping property of this set in relation to the filtration generated by the underlying Poisson process. In special cases, our general scheme yields the estimator of the volume of the convex support or the estimator of an integral of a H\\&#8221;older function. The setting is extended to higher order symmetric statistics, and it is shown that the estimation error is given by the Kabanov&#8211;Skorohod integral with respect to the underlying Poisson process. \u00a0We derive the rate of normal convergence for the estimation error, and illustrate it on an application to estimators of integrals of a H\u00f6lder function. This is a joint work with G\u00fcnter Last.<\/p>\n<p class=\"western\" lang=\"uk-UA\" align=\"justify\">\u0414\u043e\u043f\u043e\u0432\u0456\u0434\u0430\u0447:\u00a0<strong>Ilya Molchanov (University of Bern, Switzerland)<\/strong><\/p>\n<p>\u0414\u0430\u0442\u0430 \u043f\u0440\u043e\u0432\u0435\u0434\u0435\u043d\u043d\u044f: 28 \u043a\u0432\u0456\u0442\u043d\u044f 2021 \u0440\u043e\u043a\u0443 \u043e 14 \u0433\u043e\u0434 15 \u0445\u0432.<\/p>\n<div><\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>28 \u043a\u0432\u0456\u0442\u043d\u044f 2021 \u0440\u043e\u043a\u0443 \u043e 14 \u0433\u043e\u0434 15 \u0445\u0432 We consider a hull operator on Poisson point processes, the easiest example being the convex hull of the support. Assuming that theintensity measure of the process is known on the set generated by the hull operator, we discuss estimation of the expected symmetricstatistics built on the&#8230;<\/p>\n<p class=\"more-link-wrap\"><a href=\"https:\/\/do.csc.knu.ua\/?p=234\" class=\"more-link\">Read More<span class=\"screen-reader-text\"> &ldquo;Poisson Hulls&rdquo;<\/span> &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9],"tags":[],"class_list":["post-234","post","type-post","status-publish","format-standard","hentry","category-seminar"],"_links":{"self":[{"href":"https:\/\/do.csc.knu.ua\/index.php?rest_route=\/wp\/v2\/posts\/234","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/do.csc.knu.ua\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/do.csc.knu.ua\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/do.csc.knu.ua\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/do.csc.knu.ua\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=234"}],"version-history":[{"count":1,"href":"https:\/\/do.csc.knu.ua\/index.php?rest_route=\/wp\/v2\/posts\/234\/revisions"}],"predecessor-version":[{"id":1822,"href":"https:\/\/do.csc.knu.ua\/index.php?rest_route=\/wp\/v2\/posts\/234\/revisions\/1822"}],"wp:attachment":[{"href":"https:\/\/do.csc.knu.ua\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=234"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/do.csc.knu.ua\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=234"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/do.csc.knu.ua\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=234"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}