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arXiv:2501.10038 (math)
[Submitted on 17 Jan 2025]

Title:Weak uniqueness for the PDE governing the joint law of a diffusion and its running supremum

Authors:Laure Coutin (IMT), Lorick Huang (IMT), Monique Pontier (IMT)
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Abstract: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].
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:2501.10038 [math.AP]
  (or arXiv:2501.10038v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.2501.10038

Submission history

From: lorick huang [view email] [via CCSD proxy]
[v1] Fri, 17 Jan 2025 08:52:31 UTC (43 KB)
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