{"id":446346,"date":"2017-11-04T00:00:35","date_gmt":"2017-11-04T07:00:35","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/?post_type=msr-research-item&#038;p=446346"},"modified":"2017-12-04T20:21:30","modified_gmt":"2017-12-05T04:21:30","slug":"pacific-northwest-probability-seminar-random-self-similar-trees-dynamical-pruning-and-its-applications-to-inviscid-burgers-equations","status":"publish","type":"msr-video","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/video\/pacific-northwest-probability-seminar-random-self-similar-trees-dynamical-pruning-and-its-applications-to-inviscid-burgers-equations\/","title":{"rendered":"Pacific Northwest Probability Seminar: Random self-similar trees: dynamical pruning and its applications to inviscid Burgers equations"},"content":{"rendered":"<p>Consider the fractional Brownian motions on the real line. What should we expect if we replace the real line by a manifold M? We will provide an answer to this question, extending work begun by Paul Levy in 1965. We will construct a family of Gaussian processes indexed by M with certain properties and argue that these objects are the proper generalization of fractional Brownian motion to the setting of GRF-s over a manifold. We also construct analogs for the Ornstein-Uhlenbeck process indexed by M. After discussing existence, invariance, self-similarity, regularity and Hausdorff dimension, we will give some examples for different manifolds, discuss simulation, and suggest some open problems for future work.\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Consider the fractional Brownian motions on the real line. What should we expect if we replace the real line by a manifold M? We will provide an answer to this question, extending work begun by Paul Levy in 1965. We will construct a family of Gaussian processes indexed by M with certain properties and argue [&hellip;]<\/p>\n","protected":false},"featured_media":446598,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr_hide_image_in_river":0,"footnotes":""},"research-area":[13561,13546],"msr-video-type":[],"msr-locale":[268875],"msr-post-option":[],"msr-session-type":[],"msr-impact-theme":[],"msr-pillar":[],"msr-episode":[],"msr-research-theme":[],"class_list":["post-446346","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-research-area-algorithms","msr-research-area-computational-sciences-mathematics","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/VeWp2vAjerQ","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/446346","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":2,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/446346\/revisions"}],"predecessor-version":[{"id":446595,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/446346\/revisions\/446595"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/media\/446598"}],"wp:attachment":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/media?parent=446346"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=446346"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=446346"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=446346"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=446346"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=446346"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=446346"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=446346"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=446346"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=446346"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}