English

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

Analysis of PDEs 2025-01-20 v1

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].

Keywords

Cite

@article{arxiv.2501.10038,
  title  = {Weak uniqueness for the PDE governing the joint law of a diffusion and its running supremum},
  author = {Laure Coutin and Lorick Huang and Monique Pontier},
  journal= {arXiv preprint arXiv:2501.10038},
  year   = {2025}
}