{"id":{"repo_id":"wustl","oai_identifier":"oai:openscholarship.wustl.edu:etd-1074"},"canonical_url":"https://search.dev.ndltd.org/etd/wustl/oai:openscholarship.wustl.edu:etd-1074","repository":{"repo_id":"wustl","name":"Washington University in St. Louis","base_url":"https://openscholarship.wustl.edu/do/oai/"},"display":{"title":"Markov Chains Derived From Lagrangian Mechanical Systems","abstract":"The theory of Markov chains with countable state spaces is a greatly developed and successful area of probability theory and statistics. There is much interest in continuing to develop the theory of Markov chains beyond countable state spaces. One needs good and well motivated model systems in this effort. In this thesis, we propose to produce such systems by introducing randomness into familiar deterministic systems so that we can draw upon the existing: deterministic) results to aid the analysis of our Markov chains. We will focus most heavily on models drawn from Lagrangian mechanical systems with collisions: billiards).","abstract_html":"The theory of Markov chains with countable state spaces is a greatly developed and successful area of probability theory and statistics. There is much interest in continuing to develop the theory of Markov chains beyond countable state spaces. One needs good and well motivated model systems in this effort. In this thesis, we propose to produce such systems by introducing randomness into familiar deterministic systems so that we can draw upon the existing: deterministic) results to aid the analysis of our Markov chains. We will focus most heavily on models drawn from Lagrangian mechanical systems with collisions: billiards).","abstract_has_math":false,"creators":["Cook, Scott"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Renato Feres"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-01-01T08:00:00Z","date_published":"2011-01-01T08:00:00Z","updated_at":"2026-07-24T06:12:32Z","subjects":["Mathematics","Mechanics","dynamical systems","Markov chains","probabilty"],"languages":["English (en)"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.7936/K7JH3J95"],"render_values":[{"text":"https://doi.org/10.7936/K7JH3J95","href":"https://doi.org/10.7936/K7JH3J95","code":true}]}]},"links":{"outbound_url":"https://openscholarship.wustl.edu/etd/75","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Renato Feres"]},{"key":"dc:creator","label":"Author","values":["Cook, Scott"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2010-01-01T08:00:00Z"]},{"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":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","Mechanics","dynamical systems","Markov chains","probabilty"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English (en)"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://openscholarship.wustl.edu/etd/75"]},{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.7936/K7JH3J95"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The theory of Markov chains with countable state spaces is a greatly developed and successful area of probability theory and statistics. There is much interest in continuing to develop the theory of Markov chains beyond countable state spaces. One needs good and well motivated model systems in this effort. In this thesis, we propose to produce such systems by introducing randomness into familiar deterministic systems so that we can draw upon the existing: deterministic) results to aid the analysis of our Markov chains. We will focus most heavily on models drawn from Lagrangian mechanical systems with collisions: billiards)."]},{"key":"dc:title","label":"Title","values":["Markov Chains Derived From Lagrangian Mechanical Systems"]}]}],"canonical_facts":{"dc:contributor":["Renato Feres"],"dc:creator":["Cook, Scott"],"dc:date.available":["2010-01-01T08:00:00Z"],"dc:description.abstract":["The theory of Markov chains with countable state spaces is a greatly developed and successful area of probability theory and statistics. There is much interest in continuing to develop the theory of Markov chains beyond countable state spaces. One needs good and well motivated model systems in this effort. In this thesis, we propose to produce such systems by introducing randomness into familiar deterministic systems so that we can draw upon the existing: deterministic) results to aid the analysis of our Markov chains. We will focus most heavily on models drawn from Lagrangian mechanical systems with collisions: billiards)."],"dc:identifier":["https://openscholarship.wustl.edu/etd/75"],"dc:identifier.doi":["https://doi.org/10.7936/K7JH3J95"],"dc:language":["English (en)"],"dc:subject":["Mathematics","Mechanics","dynamical systems","Markov chains","probabilty"],"dc:title":["Markov Chains Derived From Lagrangian Mechanical Systems"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T06:12:32Z"}