Brownian Convergence of Planar Domains and Stability of the Planar Skorokhod Embedding Problem
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913161487056896 |
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| author | Boudabra, Maher Becher, Mrabet Haggui, Fathi |
| author_facet | Boudabra, Maher Becher, Mrabet Haggui, Fathi |
| contents | We present a numerical framework for approximating the $μ$-domain in the planar Skorokhod embedding problem PSEP, recently introduced in \cite{gross2019}. We show that under weak convergence of a sequence of probability measures $(μ_{n})_{n}$, the corresponding sequence of $μ_{n}$-domains converges, in an appropriate sense, to the domain associated with the limit measure $μ$. In addition, we provide implementation strategies, convergence rate estimates, and a numerical example. The method is robust and versatile, offering a concrete computational approach for the approximation of $μ$-domains. As part of this analysis, we introduce a novel mode of convergence for planar domains via planar Brownian motion, which we call $p$-Brownian convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25762 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Brownian Convergence of Planar Domains and Stability of the Planar Skorokhod Embedding Problem Boudabra, Maher Becher, Mrabet Haggui, Fathi Probability 60J65, 65E10, 30C35 We present a numerical framework for approximating the $μ$-domain in the planar Skorokhod embedding problem PSEP, recently introduced in \cite{gross2019}. We show that under weak convergence of a sequence of probability measures $(μ_{n})_{n}$, the corresponding sequence of $μ_{n}$-domains converges, in an appropriate sense, to the domain associated with the limit measure $μ$. In addition, we provide implementation strategies, convergence rate estimates, and a numerical example. The method is robust and versatile, offering a concrete computational approach for the approximation of $μ$-domains. As part of this analysis, we introduce a novel mode of convergence for planar domains via planar Brownian motion, which we call $p$-Brownian convergence. |
| title | Brownian Convergence of Planar Domains and Stability of the Planar Skorokhod Embedding Problem |
| topic | Probability 60J65, 65E10, 30C35 |
| url | https://arxiv.org/abs/2605.25762 |