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arXiv · 2601.10539

Smoothness of martingale observables and generalized Feynman-Kac formulas

Alex Karrila·Lauri Viitasaari
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Abstract

We prove that, under the H\"ormander criterion on an It\^{o} 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 It\^{o} calculus.

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BibTeXRIS

Alex Karrila, Lauri Viitasaari. 2026-01-15. Smoothness of martingale observables and generalized Feynman-Kac formulas. https://arxiv.org/abs/2601.10539

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