An extended variational setting for critical SPDEs with L{é}vy noise Article Swipe

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Sebastian Bechtel , Fabian Germ , Mark Veraar ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2412.17420

The critical variational setting was recently introduced and shown to be applicable to many important SPDEs not covered by the classical variational setting. In this paper, we extend the critical variational setting in several ways. We introduce a flexibility in the range space for the nonlinear drift term, due to which certain borderline cases can now also be included. An example of this is the Allen-Cahn equation in dimension two in the weak setting. In addition to this, we allow the drift to be singular in time, which is something that naturally arises in the study of the skeleton equations for large deviation principles for SPDEs. Last but not least, we present the theory in the case of L{é}vy noise for which the critical setting was not available yet.

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2412.17420
PDF: https://arxiv.org/pdf/2412.17420
OA Status: green
Related Works: 10
OpenAlex ID: https://openalex.org/W4405707554

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DOI: https://doi.org/10.48550/arxiv.2412.17420

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Title: An extended variational setting for critical SPDEs with L{é}vy noise

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Type: preprint

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Language: en

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Publication year: 2024

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Publication date: 2024-12-23

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Authors: Sebastian Bechtel, Fabian Germ, Mark Veraar

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Landing page: https://arxiv.org/abs/2412.17420

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PDF URL: https://arxiv.org/pdf/2412.17420

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Concepts: Noise (video), Applied mathematics, Mathematics, Statistical physics, Physics, Computer science, Artificial intelligence, Image (mathematics)

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