Weak uniqueness for the PDE governing the joint law of a diffusion and its running supremum
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913654681632768 |
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| author | Coutin, Laure Huang, Lorick Pontier, Monique |
| author_facet | Coutin, Laure Huang, Lorick Pontier, Monique |
| contents | In a previous work [8], it was shown that the joint law of a diffusion process and the running supremum of its first component is absolutely continuous, and that its density satisfies a non standard weak partial differential equation (PDE). In this paper, we establish the uniqueness of the solution to this PDE, providing a more complete understanding of the system's behavior and further validating the approach introduced in [8]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10038 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak uniqueness for the PDE governing the joint law of a diffusion and its running supremum Coutin, Laure Huang, Lorick Pontier, Monique Analysis of PDEs In a previous work [8], it was shown that the joint law of a diffusion process and the running supremum of its first component is absolutely continuous, and that its density satisfies a non standard weak partial differential equation (PDE). In this paper, we establish the uniqueness of the solution to this PDE, providing a more complete understanding of the system's behavior and further validating the approach introduced in [8]. |
| title | Weak uniqueness for the PDE governing the joint law of a diffusion and its running supremum |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.10038 |