{"id":{"repo_id":"ohiolink","oai_identifier":"oai:etd.ohiolink.edu:case1363709622"},"canonical_url":"https://search.dev.ndltd.org/etd/ohiolink/oai:etd.ohiolink.edu:case1363709622","repository":{"repo_id":"ohiolink","name":"OhioLINK","base_url":"https://etd.ohiolink.edu/acprod/odb_etd/ws/oai/oai"},"display":{"title":"TOPICS IN STOCHASTICS AND STATISTICS: SHOCK CREATION AND DISSOLUTION FOR STABLE AND LINNIK CONSERVATION LAWS AND TARGET STUDENT RECRUITMENT USING PREDICTIVE MODELING","abstract":"The dissertation consists of two separate parts. The first studies a theoretical problem of creation and dissolution of discontinuities (shocks) for the solutions of nonlinear integro-differential equations with diffusive terms related to the stable and Linnik processes. The second is applied, and relies on logistic models.Over the past several decades, the subject of non-local, pseudo-differential operators witnessed a considerable research activity including, for example, in application to mathematical finance and dislocation dynamics. Moreover, it has evolved into a vital and important part of the theory of conservation laws. It is known from recent work that the solutions of the fractal conservation laws exhibit shocks for bounded, odd, and convex on R+ initial data when the parameter λ<1 We study the analogous situation for the Linnik conservation laws. In the process, we investigate the relevant stochastic integrals, Orlicz spaces, infinitesimal operators and pseudo - differential operators. For nonlinear nonlocal evolution equations driven by Linnik diffusions no general rigorous mathematical results are available. Therefore, we also develop simulations and large-scale numerical methods of Linnik-Lévy conservation laws with respect to Riemann, piecewise linear, and continuous initial conditions. The main discovery here is that, despite their similar heavy tail behavior, the conservation laws driven by stable diffusions produce shocks in solutions that dissipate over time, while the Linnik diffusions do not. We formulate conjectures based on these numerical experiments.In addition, we conduct research on an applied statistics '&amp;amp;amp;apos;Factors Affecting a Student's Decision to Admit in The Law School, Case Western Reserve University'&amp;amp;amp;apos; project and determine the predictors for the minimum amount of scholarship award that is needed to admit the best prospective students in the Case Western Reserve University Law school program.","abstract_html":"The dissertation consists of two separate parts. The first studies a theoretical problem of creation and dissolution of discontinuities (shocks) for the solutions of nonlinear integro-differential equations with diffusive terms related to the stable and Linnik processes. The second is applied, and relies on logistic models.Over the past several decades, the subject of non-local, pseudo-differential operators witnessed a considerable research activity including, for example, in application to mathematical finance and dislocation dynamics. Moreover, it has evolved into a vital and important part of the theory of conservation laws. It is known from recent work that the solutions of the fractal conservation laws exhibit shocks for bounded, odd, and convex on <b>R<sup>+</sup></b> initial data when the parameter λ<1 We study the analogous situation for the Linnik conservation laws. In the process, we investigate the relevant stochastic integrals, Orlicz spaces, infinitesimal operators and pseudo - differential operators. For nonlinear nonlocal evolution equations driven by Linnik diffusions no general rigorous mathematical results are available. Therefore, we also develop simulations and large-scale numerical methods of Linnik-Lévy conservation laws with respect to Riemann, piecewise linear, and continuous initial conditions. The main discovery here is that, despite their similar heavy tail behavior, the conservation laws driven by stable diffusions produce shocks in solutions that dissipate over time, while the Linnik diffusions do not. We formulate conjectures based on these numerical experiments.In addition, we conduct research on an applied statistics '&amp;amp;amp;amp;apos;Factors Affecting a Student's Decision to Admit in The Law School, Case Western Reserve University'&amp;amp;amp;amp;apos; project and determine the predictors for the minimum amount of scholarship award that is needed to admit the best prospective students in the Case Western Reserve University Law school program.","abstract_has_math":false,"creators":["Gunaratnam, Bakeerathan"],"institution":"Case Western Reserve University School of Graduate Studies","degree_name":"Doctor of Philosophy","degree_level":"doctoral","degree_discipline":"Statistics","degree_department":null,"school":null,"contributors":["Woyczynski, Wojbor"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-08-16","date_published":"2013-08-16","updated_at":"2026-07-24T03:37:01Z","subjects":["Statistics"],"languages":["English"],"rights":["unrestricted","This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://rave.ohiolink.edu/etdc/view?acc_num=case1363709622","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Woyczynski, Wojbor"]},{"key":"dc:creator","label":"Author","values":["Gunaratnam, Bakeerathan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2013-08-16"]},{"key":"dc:publisher","label":"Institution","values":["Case Western Reserve University School of Graduate Studies / OhioLINK"]},{"key":"dc:type","label":"Dc Type","values":["Electronic Thesis or Dissertation"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Case Western Reserve University School of Graduate Studies"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Statistics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]},{"key":"dc:rights","label":"Dc Rights","values":["unrestricted","This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://rave.ohiolink.edu/etdc/view?acc_num=case1363709622"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The dissertation consists of two separate parts. The first studies a theoretical problem of creation and dissolution of discontinuities (shocks) for the solutions of nonlinear integro-differential equations with diffusive terms related to the stable and Linnik processes. The second is applied, and relies on logistic models.Over the past several decades, the subject of non-local, pseudo-differential operators witnessed a considerable research activity including, for example, in application to mathematical finance and dislocation dynamics. Moreover, it has evolved into a vital and important part of the theory of conservation laws. It is known from recent work that the solutions of the fractal conservation laws exhibit shocks for bounded, odd, and convex on R+ initial data when the parameter λ<1 We study the analogous situation for the Linnik conservation laws. In the process, we investigate the relevant stochastic integrals, Orlicz spaces, infinitesimal operators and pseudo - differential operators. For nonlinear nonlocal evolution equations driven by Linnik diffusions no general rigorous mathematical results are available. Therefore, we also develop simulations and large-scale numerical methods of Linnik-Lévy conservation laws with respect to Riemann, piecewise linear, and continuous initial conditions. The main discovery here is that, despite their similar heavy tail behavior, the conservation laws driven by stable diffusions produce shocks in solutions that dissipate over time, while the Linnik diffusions do not. We formulate conjectures based on these numerical experiments.In addition, we conduct research on an applied statistics '&amp;amp;amp;apos;Factors Affecting a Student's Decision to Admit in The Law School, Case Western Reserve University'&amp;amp;amp;apos; project and determine the predictors for the minimum amount of scholarship award that is needed to admit the best prospective students in the Case Western Reserve University Law school program."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf","p.126","1.47 MB"]},{"key":"dc:title","label":"Title","values":["TOPICS IN STOCHASTICS AND STATISTICS: SHOCK CREATION AND DISSOLUTION FOR STABLE AND LINNIK CONSERVATION LAWS AND TARGET STUDENT RECRUITMENT USING PREDICTIVE MODELING"]}]}],"canonical_facts":{"dc:contributor":["Woyczynski, Wojbor"],"dc:creator":["Gunaratnam, Bakeerathan"],"dc:date":["2013-08-16"],"dc:description":["The dissertation consists of two separate parts. The first studies a theoretical problem of creation and dissolution of discontinuities (shocks) for the solutions of nonlinear integro-differential equations with diffusive terms related to the stable and Linnik processes. The second is applied, and relies on logistic models.Over the past several decades, the subject of non-local, pseudo-differential operators witnessed a considerable research activity including, for example, in application to mathematical finance and dislocation dynamics. Moreover, it has evolved into a vital and important part of the theory of conservation laws. It is known from recent work that the solutions of the fractal conservation laws exhibit shocks for bounded, odd, and convex on R+ initial data when the parameter λ<1 We study the analogous situation for the Linnik conservation laws. In the process, we investigate the relevant stochastic integrals, Orlicz spaces, infinitesimal operators and pseudo - differential operators. For nonlinear nonlocal evolution equations driven by Linnik diffusions no general rigorous mathematical results are available. Therefore, we also develop simulations and large-scale numerical methods of Linnik-Lévy conservation laws with respect to Riemann, piecewise linear, and continuous initial conditions. The main discovery here is that, despite their similar heavy tail behavior, the conservation laws driven by stable diffusions produce shocks in solutions that dissipate over time, while the Linnik diffusions do not. We formulate conjectures based on these numerical experiments.In addition, we conduct research on an applied statistics '&amp;amp;amp;apos;Factors Affecting a Student's Decision to Admit in The Law School, Case Western Reserve University'&amp;amp;amp;apos; project and determine the predictors for the minimum amount of scholarship award that is needed to admit the best prospective students in the Case Western Reserve University Law school program."],"dc:format":["application/pdf","p.126","1.47 MB"],"dc:identifier":["http://rave.ohiolink.edu/etdc/view?acc_num=case1363709622"],"dc:language":["English"],"dc:publisher":["Case Western Reserve University School of Graduate Studies / OhioLINK"],"dc:rights":["unrestricted","This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws."],"dc:subject":["Statistics"],"dc:title":["TOPICS IN STOCHASTICS AND STATISTICS: SHOCK CREATION AND DISSOLUTION FOR STABLE AND LINNIK CONSERVATION LAWS AND TARGET STUDENT RECRUITMENT USING PREDICTIVE MODELING"],"dc:type":["Electronic Thesis or Dissertation"],"thesis:degree_discipline":["Statistics"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["Case Western Reserve University School of Graduate Studies"]},"updated_at":"2026-07-24T03:37:01Z"}