Comparison of viscosity solutions for a class of second order PDEs on the Wasserstein space
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| Format: | Preprint |
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2023
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| _version_ | 1866913545874046976 |
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| author | Bayraktar, Erhan Ekren, Ibrahim Zhang, Xin |
| author_facet | Bayraktar, Erhan Ekren, Ibrahim Zhang, Xin |
| contents | We prove a comparison result for viscosity solutions of second order parabolic partial differential equations in the Wasserstein space. The comparison is valid for semisolutions that are Lipschitz continuous in the measure in a Fourier-Wasserstein metric and uniformly continuous in time. The class of equations we consider is motivated by Mckean-Vlasov control problems with common noise and filtering problems. The proof of comparison relies on a novel version of Ishii's lemma, which is tailor-made for the class of equations we consider. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_05040 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Comparison of viscosity solutions for a class of second order PDEs on the Wasserstein space Bayraktar, Erhan Ekren, Ibrahim Zhang, Xin Analysis of PDEs Optimization and Control Probability 58E30, 90C05 We prove a comparison result for viscosity solutions of second order parabolic partial differential equations in the Wasserstein space. The comparison is valid for semisolutions that are Lipschitz continuous in the measure in a Fourier-Wasserstein metric and uniformly continuous in time. The class of equations we consider is motivated by Mckean-Vlasov control problems with common noise and filtering problems. The proof of comparison relies on a novel version of Ishii's lemma, which is tailor-made for the class of equations we consider. |
| title | Comparison of viscosity solutions for a class of second order PDEs on the Wasserstein space |
| topic | Analysis of PDEs Optimization and Control Probability 58E30, 90C05 |
| url | https://arxiv.org/abs/2309.05040 |