Solution theory of fractional SDEs in complete subcritical regimes
We consider stochastic differential equations (SDEs) driven by a fractional Brownian motion with a drift coefficient that is allowed to be arbitrarily close to criticality in a scaling sense. We develop a comprehensive solution theory that includes strong existence, path-by-path uniqueness, existenc...
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| Language: | English |
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Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509424001361/type/journal_article |
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| author | Lucio Galeati Máté Gerencsér |
| author_facet | Lucio Galeati Máté Gerencsér |
| author_sort | Lucio Galeati |
| collection | DOAJ |
| description | We consider stochastic differential equations (SDEs) driven by a fractional Brownian motion with a drift coefficient that is allowed to be arbitrarily close to criticality in a scaling sense. We develop a comprehensive solution theory that includes strong existence, path-by-path uniqueness, existence of a solution flow of diffeomorphisms, Malliavin differentiability and
$\rho $
-irregularity. As a consequence, we can also treat McKean-Vlasov, transport and continuity equations. |
| format | Article |
| id | doaj-art-04d2743b5aac416dbcbbbc6d1b437e04 |
| institution | Kabale University |
| issn | 2050-5094 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj-art-04d2743b5aac416dbcbbbc6d1b437e042025-01-24T05:20:15ZengCambridge University PressForum of Mathematics, Sigma2050-50942025-01-011310.1017/fms.2024.136Solution theory of fractional SDEs in complete subcritical regimesLucio Galeati0https://orcid.org/0000-0001-8187-9245Máté Gerencsér1https://orcid.org/0000-0002-7276-7054Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica, Università degli Studi dell’Aquila, Edificio Renato Ricamo, via Vetoio, Coppito, L’Aquila, 67100, Italy; E-mail:Institute of Analysis and Scientific Computing, TU Wien, Wiedner Hauptstraße 8–10, Vienna, 1040, Austria;We consider stochastic differential equations (SDEs) driven by a fractional Brownian motion with a drift coefficient that is allowed to be arbitrarily close to criticality in a scaling sense. We develop a comprehensive solution theory that includes strong existence, path-by-path uniqueness, existence of a solution flow of diffeomorphisms, Malliavin differentiability and $\rho $ -irregularity. As a consequence, we can also treat McKean-Vlasov, transport and continuity equations.https://www.cambridge.org/core/product/identifier/S2050509424001361/type/journal_article60H5035R6060G22 |
| spellingShingle | Lucio Galeati Máté Gerencsér Solution theory of fractional SDEs in complete subcritical regimes Forum of Mathematics, Sigma 60H50 35R60 60G22 |
| title | Solution theory of fractional SDEs in complete subcritical regimes |
| title_full | Solution theory of fractional SDEs in complete subcritical regimes |
| title_fullStr | Solution theory of fractional SDEs in complete subcritical regimes |
| title_full_unstemmed | Solution theory of fractional SDEs in complete subcritical regimes |
| title_short | Solution theory of fractional SDEs in complete subcritical regimes |
| title_sort | solution theory of fractional sdes in complete subcritical regimes |
| topic | 60H50 35R60 60G22 |
| url | https://www.cambridge.org/core/product/identifier/S2050509424001361/type/journal_article |
| work_keys_str_mv | AT luciogaleati solutiontheoryoffractionalsdesincompletesubcriticalregimes AT mategerencser solutiontheoryoffractionalsdesincompletesubcriticalregimes |