{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/34446"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/34446","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Stochastic stability of replicator dynamics with random jumps","abstract":"We further generalize the stochastic version of the replicator dynamics due to Fudenberg and Harris. In particular, we add a random jump term to the payo ff function to simulate anomalous events and their e ffects on the fi tness. Assuming a 2 by 2 game and using a particular characteristic of the jump functions we are able to estimate the ergodic measure for all games. Lastly, working with results and methods developed by Imhoff, we prove some stability theorems for an arbitrary n by n game.","abstract_html":"We further generalize the stochastic version of the replicator dynamics due to Fudenberg and Harris. In particular, we add a random jump term to the payo ff function to simulate anomalous events and their e ffects on the fi tness. Assuming a 2 by 2 game and using a particular characteristic of the jump functions we are able to estimate the ergodic measure for all games. Lastly, working with results and methods developed by Imhoff, we prove some stability theorems for an arbitrary n by n game.","abstract_has_math":false,"creators":["Vlasic, Andrew"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Muncaster, Robert G.","Song, Renming","Bauer, Robert","Rapti, Zoi"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-09-18T21:17:35Z","date_published":"2012-09-18T21:17:35Z","updated_at":"2026-07-22T22:25:31Z","subjects":["Asymptotic stochastic stability","evolutionarily stable strategy","invariant measure","Lyapunov function","Nash equilibrium","recurrence","stochastic differential equation"],"languages":["en"],"rights":["Copyright 2012 Andrew Vlasic"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/34446","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Muncaster, Robert G.","Song, Renming","Bauer, Robert","Rapti, Zoi"]},{"key":"dc:creator","label":"Author","values":["Vlasic, Andrew"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2012-09-18T21:17:35Z","2014-09-18T10:00:58Z","2012-08"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Asymptotic stochastic stability","evolutionarily stable strategy","invariant measure","Lyapunov function","Nash equilibrium","recurrence","stochastic differential equation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2012 Andrew Vlasic"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/34446"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We further generalize the stochastic version of the replicator dynamics due to Fudenberg and Harris. In particular, we add a random jump term to the payo ff function to simulate anomalous events and their e ffects on the fi tness. Assuming a 2 by 2 game and using a particular characteristic of the jump functions we are able to estimate the ergodic measure for all games. Lastly, working with results and methods developed by Imhoff, we prove some stability theorems for an arbitrary n by n game.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-07-06T18:32:29Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 2 Thesis Write Up.tex: 186601 bytes, checksum: f08fbeef56e24e61b792e9ca4b9398e6 (MD5) Vlasic_Andrew.pdf: 12676540 bytes, checksum: f3d6f4e842d0eaa0702f32ef92d5238a (MD5)","Made available in DSpace on 2012-09-18T21:17:35Z (GMT). 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In particular, we add a random jump term to the payo ff function to simulate anomalous events and their e ffects on the fi tness. Assuming a 2 by 2 game and using a particular characteristic of the jump functions we are able to estimate the ergodic measure for all games. Lastly, working with results and methods developed by Imhoff, we prove some stability theorems for an arbitrary n by n game.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-07-06T18:32:29Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 2 Thesis Write Up.tex: 186601 bytes, checksum: f08fbeef56e24e61b792e9ca4b9398e6 (MD5) Vlasic_Andrew.pdf: 12676540 bytes, checksum: f3d6f4e842d0eaa0702f32ef92d5238a (MD5)","Made available in DSpace on 2012-09-18T21:17:35Z (GMT). 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