{"id":6326,"date":"2026-10-19T09:48:46","date_gmt":"2026-10-19T09:48:46","guid":{"rendered":"https:\/\/phd.hi.is\/doktorsvorn\/doktorsvorn-i-staerdfraedi-hjortur-bjornsson\/"},"modified":"2026-10-19T09:48:46","modified_gmt":"2026-10-19T09:48:46","slug":"doktorsvorn-i-staerdfraedi-hjortur-bjornsson","status":"publish","type":"phd_defence","link":"https:\/\/phd.hi.is\/en\/doktorsvorn\/doktorsvorn-i-staerdfraedi-hjortur-bjornsson\/","title":{"rendered":"Doktorsv\u00f6rn \u00ed st\u00e6r\u00f0fr\u00e6\u00f0i \u2013 Hj\u00f6rtur Bj\u00f6rnsson"},"content":{"rendered":"<div class=\"field-items\">\n<div class=\"field-item even\" property=\"content:encoded\">\n<p><strong>Doktorsefni:<\/strong>\u00a0Hj\u00f6rtur Bj\u00f6rnsson<\/p>\n<p><strong>Heiti ritger\u00f0ar:\u00a0<\/strong>Lyapunov f\u00f6ll og slembin kerfi: Fr\u00e6\u00f0i og t\u00f6lulegar a\u00f0fer\u00f0ir (Lyapunov Functions for Stochastic Systems: Theory and Numerics)<\/p>\n<p><strong>Lei\u00f0beinandi:\u00a0<\/strong>Dr. Sigur\u00f0ur Freyr Hafstein, pr\u00f3fessor vi\u00f0 Raunv\u00edsindadeild H\u00cd<\/p>\n<p><strong>Einnig \u00ed doktorsnefnd:\u00a0<br \/> <\/strong>Dr. Sigur\u00f0ur \u00d6rn Stef\u00e1nsson, pr\u00f3fessor vi\u00f0 Raunv\u00edsindadeild H\u00cd<br \/> Dr. Peter Giesl, pr\u00f3fessor vi\u00f0 H\u00e1sk\u00f3lann \u00ed Sussex, Bretlandi<\/p>\n<p><strong>Andm\u00e6lendur:\u00a0<br \/> <\/strong>Dr. Gerardo Barrera Vargas, pr\u00f3fessor vi\u00f0 H\u00e1sk\u00f3lann \u00ed Helsinki, Finnlandi<br \/> Dr. Florian Rupp, pr\u00f3fessor vi\u00f0 Al\u00fej\u00f3\u00f0lega H\u00e1sk\u00f3lann \u00ed Kutaisi, Georg\u00edu<\/p>\n<p><strong>Doktorsv\u00f6rn st\u00fdrir<\/strong>:\u00a0Dr. Einar \u00d6rn Sveinbj\u00f6rnsson, pr\u00f3fessor og deildarforseti Raunv\u00edsindadeildar H\u00cd<\/p>\n<p><strong>\u00c1grip<\/strong><\/p>\n<p>\u00cd \u00feessari ritger\u00f0 munum vi\u00f0 sko\u00f0a Lyapunov f\u00f6ll fyrir slembnar diffurj\u00f6fnur. Lyapunov f\u00f6ll eru mj\u00f6g gagnleg \u00feegar vi\u00f0 k\u00f6nnum st\u00f6\u00f0ugleika jafnv\u00e6gispunkta slembna kerfa, og langt\u00edma heg\u00f0un s\u00e9rlausna \u00ed kringum \u00fe\u00e1. Vi\u00f0 fj\u00f6llum um a\u00f0fer\u00f0, til a\u00f0 reikna svokalla\u00f0 a\u00f0dr\u00e1ttarsv\u00e6\u00f0i og n\u00e1kv\u00e6mar ne\u00f0ri skor\u00f0ur, sem felst \u00ed \u00fev\u00ed a\u00f0 nota saman sta\u00f0bundi\u00f0 Lyapunov fall og \u00f3sta\u00f0bundi\u00f0 Lyapunov fall. Fyrst fj\u00f6llum vi\u00f0 um Lyapunov f\u00f6ll, fyrir n\u00e6stum \u00f6rugglega veldisa\u00f0fellust\u00f6\u00f0ug kerfi, og alh\u00e6fum \u00feau fyrir st\u00e6rra og gagnlegra fallar\u00fam. \u00cd \u00f6\u00f0ru lagi \u00fe\u00e1 fj\u00f6llum vi\u00f0 um a\u00f0fer\u00f0 til a\u00f0 reikna sta\u00f0bundin Lyapunov f\u00f6ll me\u00f0 \u00fev\u00ed a\u00f0 l\u00ednugera slembna kerfi\u00f0. \u00cd \u00feri\u00f0ja lagi, \u00fe\u00e1 reiknum vi\u00f0 \u00f3sta\u00f0bundi\u00f0 Lyapunov fall me\u00f0 t\u00f6lulegri a\u00f0fer\u00f0 sem kallast m\u00f6skvalaus samlegua\u00f0fer\u00f0. Me\u00f0 \u00feessari a\u00f0fer\u00f0 getum vi\u00f0 reikna\u00f0 \u00fat raunverulegt Lyapunov fall t\u00f6lulega \u00ed sta\u00f0 \u00feess reikna \u00fat t\u00f6lulega n\u00e1lgun. Vi\u00f0 fj\u00f6llum um reiknierfi\u00f0leika sem vi\u00f0 t\u00f3kumst \u00e1 vi\u00f0, og hvernig \u00ed framhaldinu vi\u00f0 sko\u00f0u\u00f0um Wendland f\u00f6ll og mismunandi a\u00f0fer\u00f0ir til a\u00f0 reikna \u00feau t\u00f6lulega. Ni\u00f0ursta\u00f0an var a\u00f0fer\u00f0 sem b\u00fdr til Wendland f\u00f6ll \u00ed hagkv\u00e6mri mynd og hugb\u00fana\u00f0ur sem n\u00fdtir \u00feau til a\u00f0 leysa hlutaflei\u00f0uj\u00f6fnur me\u00f0 m\u00f6svkalausri samlegua\u00f0fer\u00f0.<\/p>\n<p><strong>Um doktorsefni\u00f0<\/strong><\/p>\n<p>Hj\u00f6rtur Bj\u00f6rnsson h\u00f3f n\u00e1m vi\u00f0 H\u00e1sk\u00f3la \u00cdslands \u00e1ri\u00f0 2009 og hefur loki\u00f0 b\u00e6\u00f0i B.Sc- og M.Sc-pr\u00f3fi \u00ed st\u00e6r\u00f0fr\u00e6\u00f0i fr\u00e1 H\u00cd. Einnig var hann \u00ed skiptin\u00e1mi vi\u00f0 H\u00e1sk\u00f3lann \u00ed Gautaborg \u00ed eitt \u00e1r.<br \/> Hj\u00f6rtur hefur starfa\u00f0 sem stundarkennari vi\u00f0 H\u00e1sk\u00f3lann \u00ed Reykjav\u00edk og H\u00e1sk\u00f3la \u00cdslands samhli\u00f0a n\u00e1mi, og starfar n\u00fa vi\u00f0 \u00e1h\u00e6ttust\u00fdringu hj\u00e1 Landsbankanum.<\/p>\n<\/div><\/div>","protected":false},"featured_media":5610,"template":"","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"_phd_date_start":"2023-05-15T13:00:00+00:00","_phd_date_end":"2023-05-15T15:00:00+00:00","_phd_location":"A\u00f0albygging H\u00e1t\u00ed\u00f0arsalur","_phd_admission":"A\u00f0gangur \u00f3keypis","_phd_thesis_title":"Lyapunov f\u00f6ll og slembin kerfi: Fr\u00e6\u00f0i og t\u00f6lulegar a\u00f0fer\u00f0ir (Lyapunov Functions for Stochastic Systems: Theory and Numerics)","_phd_source_url":"https:\/\/gamli.hi.is\/vidburdir\/doktorsvorn_i_staerdfraedi_hjortur_bjornsson","_phd_source_node_id":"419803","_phd_source_type":"vidburdir","_phd_member_id":862,"footnotes":""},"phd_school":[101,93],"phd_discipline":[103],"class_list":["post-6326","phd_defence","type-phd_defence","status-publish","has-post-thumbnail","hentry","phd_school-raunvisindadeild","phd_school-verkfraedi-og-natturuvisindasvid","phd_discipline-phd-i-staerdfraedi"],"_links":{"self":[{"href":"https:\/\/phd.hi.is\/en\/wp-json\/wp\/v2\/phd_defence\/6326","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/phd.hi.is\/en\/wp-json\/wp\/v2\/phd_defence"}],"about":[{"href":"https:\/\/phd.hi.is\/en\/wp-json\/wp\/v2\/types\/phd_defence"}],"version-history":[{"count":0,"href":"https:\/\/phd.hi.is\/en\/wp-json\/wp\/v2\/phd_defence\/6326\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/phd.hi.is\/en\/wp-json\/wp\/v2\/media\/5610"}],"wp:attachment":[{"href":"https:\/\/phd.hi.is\/en\/wp-json\/wp\/v2\/media?parent=6326"}],"wp:term":[{"taxonomy":"phd_school","embeddable":true,"href":"https:\/\/phd.hi.is\/en\/wp-json\/wp\/v2\/phd_school?post=6326"},{"taxonomy":"phd_discipline","embeddable":true,"href":"https:\/\/phd.hi.is\/en\/wp-json\/wp\/v2\/phd_discipline?post=6326"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}