Uniqueness in law for singular degenerate SDEs with respect to a (sub-)invariant measure
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915288997429248 |
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| author | Lee, Haesung Trutnau, Gerald |
| author_facet | Lee, Haesung Trutnau, Gerald |
| contents | We show weak existence and uniqueness in law for a general class of stochastic differential equations in $\mathbb{R}^d$, $d\ge 1$, with prescribed sub-invariant measure $\widehatμ$. The dispersion and drift coefficients of the stochastic differential equation are allowed to be degenerate and discontinuous, and locally unbounded, respectively. Uniqueness in law is obtained via $L^1(\mathbb{R}^d,\widehatμ)$-uniqueness in a subclass of continuous Markov processes, namely right processes that have $\widehatμ$ as sub-invariant measure and have continuous paths for $\widehatμ$-almost every starting point. Weak existence is obtained for a broader class via the martingale problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14902 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniqueness in law for singular degenerate SDEs with respect to a (sub-)invariant measure Lee, Haesung Trutnau, Gerald Probability primary, 60H20, 47D07, 60J46, secondary: 60J40, 47B44, 60J35 We show weak existence and uniqueness in law for a general class of stochastic differential equations in $\mathbb{R}^d$, $d\ge 1$, with prescribed sub-invariant measure $\widehatμ$. The dispersion and drift coefficients of the stochastic differential equation are allowed to be degenerate and discontinuous, and locally unbounded, respectively. Uniqueness in law is obtained via $L^1(\mathbb{R}^d,\widehatμ)$-uniqueness in a subclass of continuous Markov processes, namely right processes that have $\widehatμ$ as sub-invariant measure and have continuous paths for $\widehatμ$-almost every starting point. Weak existence is obtained for a broader class via the martingale problem. |
| title | Uniqueness in law for singular degenerate SDEs with respect to a (sub-)invariant measure |
| topic | Probability primary, 60H20, 47D07, 60J46, secondary: 60J40, 47B44, 60J35 |
| url | https://arxiv.org/abs/2404.14902 |