Smoothness of martingale observables and generalized Feynman-Kac formulas
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914526830526464 |
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| author | Karrila, Alex Viitasaari, Lauri |
| author_facet | Karrila, Alex Viitasaari, Lauri |
| contents | We prove that, under the Hörmander criterion on an Itô process, all its martingale observables are smooth. As a consequence, we also obtain a generalized Feynman-Kac formula providing smooth solutions to certain PDE boundary-value problems, while allowing for degenerate diffusions as well as boundary stopping (under very mild boundary regularity assumptions). We also highlight an application to a question posed on Schramm-Loewner evolutions, by making certain Girsanov transform martingales accessible via Itô calculus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10539 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Smoothness of martingale observables and generalized Feynman-Kac formulas Karrila, Alex Viitasaari, Lauri Probability Mathematical Physics Analysis of PDEs 60H10, 60H30, 60J67, 60G44 We prove that, under the Hörmander criterion on an Itô process, all its martingale observables are smooth. As a consequence, we also obtain a generalized Feynman-Kac formula providing smooth solutions to certain PDE boundary-value problems, while allowing for degenerate diffusions as well as boundary stopping (under very mild boundary regularity assumptions). We also highlight an application to a question posed on Schramm-Loewner evolutions, by making certain Girsanov transform martingales accessible via Itô calculus. |
| title | Smoothness of martingale observables and generalized Feynman-Kac formulas |
| topic | Probability Mathematical Physics Analysis of PDEs 60H10, 60H30, 60J67, 60G44 |
| url | https://arxiv.org/abs/2601.10539 |