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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2303.10038 |
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| _version_ | 1866910779813396480 |
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| author | Wessels, Lukas |
| author_facet | Wessels, Lukas |
| contents | We prove the existence of a $B$-continuous viscosity solution for a class of infinite dimensional semilinear partial differential equations (PDEs) using probabilistic methods. Our approach also yields a stochastic representation formula for the solution in terms of a scalar-valued backward stochastic differential equation. The uniqueness is proved under additional assumptions using a comparison theorem for viscosity solutions. Our results constitute the first nonlinear Feynman-Kac formula using the notion of $B$-continuous viscosity solutions and thus introduces a framework allowing for generalizations to the case of fully nonlinear PDEs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_10038 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Semilinear Feynman-Kac Formulae for $B$-Continuous Viscosity Solutions Wessels, Lukas Probability Analysis of PDEs We prove the existence of a $B$-continuous viscosity solution for a class of infinite dimensional semilinear partial differential equations (PDEs) using probabilistic methods. Our approach also yields a stochastic representation formula for the solution in terms of a scalar-valued backward stochastic differential equation. The uniqueness is proved under additional assumptions using a comparison theorem for viscosity solutions. Our results constitute the first nonlinear Feynman-Kac formula using the notion of $B$-continuous viscosity solutions and thus introduces a framework allowing for generalizations to the case of fully nonlinear PDEs. |
| title | Semilinear Feynman-Kac Formulae for $B$-Continuous Viscosity Solutions |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2303.10038 |