Solution theory of fractional SDEs in complete subcritical regimes
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909467263631360 |
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| author | Galeati, Lucio Gerencsér, Máté |
| author_facet | Galeati, Lucio Gerencsér, Máté |
| contents | 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 $ρ$-irregularity. As a consequence, we can also treat McKean-Vlasov, transport and continuity equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_03475 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Solution theory of fractional SDEs in complete subcritical regimes Galeati, Lucio Gerencsér, Máté Probability Analysis of PDEs Primary: 60H50. Secondary: 35R60, 60G22 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 $ρ$-irregularity. As a consequence, we can also treat McKean-Vlasov, transport and continuity equations. |
| title | Solution theory of fractional SDEs in complete subcritical regimes |
| topic | Probability Analysis of PDEs Primary: 60H50. Secondary: 35R60, 60G22 |
| url | https://arxiv.org/abs/2207.03475 |