Abstract:We present a numerical framework for approximating the $\mu$-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 $(\mu_{n})_{n}$, the corresponding sequence of $\mu_{n}$-domains converges, in an appropriate sense, to the domain associated with the limit measure $\mu$. 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 $\mu$-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.
| Comments: | To appear in Archiv der Mathematik (in press) |
| Subjects: | Probability (math.PR) |
| MSC classes: | 60J65, 65E10, 30C35 |
| Cite as: | arXiv:2605.25762 [math.PR] |
| (or arXiv:2605.25762v1 [math.PR] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25762 arXiv-issued DOI via DataCite (pending registration) |
From: Maher Boudabra [view email]
[v1]
Mon, 25 May 2026 12:17:03 UTC (169 KB)
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