McKean-Vlasov Equations with Positive Feedback through Elastic Stopping Times
We prove existence and uniqueness of physical and minimal solutions to McKean-Vlasov equations with positive feedback through elastic stopping times. We do this by establishing a relationship between this problem and a problem with absorbing stopping times. We show convergence of a particle system t...
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| creator | Hambly, Ben Meier, Julian |
| description | We prove existence and uniqueness of physical and minimal solutions to
McKean-Vlasov equations with positive feedback through elastic stopping times.
We do this by establishing a relationship between this problem and a problem
with absorbing stopping times. We show convergence of a particle system to the
McKean-Vlasov equation. Moreover, we establish convergence of the elastic
McKean-Vlasov problem to the problem with absorbing stopping times and to a
reflecting Brownian motion as the elastic parameter goes to infinity or zero
respectively. |
| doi_str_mv | 10.48550/arxiv.2203.10787 |
| format | Article |
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McKean-Vlasov equations with positive feedback through elastic stopping times.
We do this by establishing a relationship between this problem and a problem
with absorbing stopping times. We show convergence of a particle system to the
McKean-Vlasov equation. Moreover, we establish convergence of the elastic
McKean-Vlasov problem to the problem with absorbing stopping times and to a
reflecting Brownian motion as the elastic parameter goes to infinity or zero
respectively.</description><identifier>DOI: 10.48550/arxiv.2203.10787</identifier><language>eng</language><subject>Mathematics - Probability</subject><creationdate>2022-03</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2203.10787$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2203.10787$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Hambly, Ben</creatorcontrib><creatorcontrib>Meier, Julian</creatorcontrib><title>McKean-Vlasov Equations with Positive Feedback through Elastic Stopping Times</title><description>We prove existence and uniqueness of physical and minimal solutions to
McKean-Vlasov equations with positive feedback through elastic stopping times.
We do this by establishing a relationship between this problem and a problem
with absorbing stopping times. We show convergence of a particle system to the
McKean-Vlasov equation. Moreover, we establish convergence of the elastic
McKean-Vlasov problem to the problem with absorbing stopping times and to a
reflecting Brownian motion as the elastic parameter goes to infinity or zero
respectively.</description><subject>Mathematics - Probability</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz71OwzAYhWEvDKhwAUz4BhIc_8TJiKoUEK1AImKNPttfGos2CbEb4O5pC9NZXh3pIeQmY6kslGJ3MH37OeWciTRjutCXZLOxzwh98r6DMMy0-jxA9EMf6JePHX0dgo9-RrpCdAbsB43dNBy2Ha2OffSWvsVhHH2_pbXfY7giFy3sAl7_74LUq6pePibrl4en5f06gVzrRICSmAkFHIVEZqwq29JxowAYcMhz3hbKGX5spFGOOaONy9DY0uayYFosyO3f7dnTjJPfw_TTnFzN2SV-AXpQSTk</recordid><startdate>20220321</startdate><enddate>20220321</enddate><creator>Hambly, Ben</creator><creator>Meier, Julian</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20220321</creationdate><title>McKean-Vlasov Equations with Positive Feedback through Elastic Stopping Times</title><author>Hambly, Ben ; Meier, Julian</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a677-3a54e135a2e34e0bc59f9d2b5aa0a2a662f85db2e134b5d0db7bd1ebc9c648073</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Mathematics - Probability</topic><toplevel>online_resources</toplevel><creatorcontrib>Hambly, Ben</creatorcontrib><creatorcontrib>Meier, Julian</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Hambly, Ben</au><au>Meier, Julian</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>McKean-Vlasov Equations with Positive Feedback through Elastic Stopping Times</atitle><date>2022-03-21</date><risdate>2022</risdate><abstract>We prove existence and uniqueness of physical and minimal solutions to
McKean-Vlasov equations with positive feedback through elastic stopping times.
We do this by establishing a relationship between this problem and a problem
with absorbing stopping times. We show convergence of a particle system to the
McKean-Vlasov equation. Moreover, we establish convergence of the elastic
McKean-Vlasov problem to the problem with absorbing stopping times and to a
reflecting Brownian motion as the elastic parameter goes to infinity or zero
respectively.</abstract><doi>10.48550/arxiv.2203.10787</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Probability |
| title | McKean-Vlasov Equations with Positive Feedback through Elastic Stopping Times |
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