A note on the planar Skorokhod embedding problem
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909972433993728 |
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| author | Boudabra, Maher |
| author_facet | Boudabra, Maher |
| contents | The planar Skorokhod embedding problem was first proposed and solved by R. Gross in 2019 [#gross2019]. Gross worked with probability distributions having finite second moment. In [#boudabra2019remarks, #Boudabra2020], the solutions extended to all distributions with a finite $p^{th}$ moment for $p>1$. The case $p=1$ remained uncovered since then. In this note we show that the planar Skorokhod embedding problem is solvable for $p=1$ when the Hilbert transform of its quantile function is integrable, effectively closing this line of investigation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18353 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on the planar Skorokhod embedding problem Boudabra, Maher Probability 30C35, 60D05, 51M25 The planar Skorokhod embedding problem was first proposed and solved by R. Gross in 2019 [#gross2019]. Gross worked with probability distributions having finite second moment. In [#boudabra2019remarks, #Boudabra2020], the solutions extended to all distributions with a finite $p^{th}$ moment for $p>1$. The case $p=1$ remained uncovered since then. In this note we show that the planar Skorokhod embedding problem is solvable for $p=1$ when the Hilbert transform of its quantile function is integrable, effectively closing this line of investigation. |
| title | A note on the planar Skorokhod embedding problem |
| topic | Probability 30C35, 60D05, 51M25 |
| url | https://arxiv.org/abs/2512.18353 |