A stochastic Schauder-Tychonoff type theorem and its applications
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918347087544320 |
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| author | Hausenblas, Erika Kumar, Ankit Tölle, Jonas M. |
| author_facet | Hausenblas, Erika Kumar, Ankit Tölle, Jonas M. |
| contents | One standard way to prove existence for deterministic, highly nonlinear PDEs is to use the Schauder-Tychonoff fixed-point theorem. In what follows, we introduce and verify a stochastic variant of the Schauder-Tychonoff theorem. We apply our existence result to nonlinear stochastic diffusion equations with non-Lipschitz perturbations |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17285 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A stochastic Schauder-Tychonoff type theorem and its applications Hausenblas, Erika Kumar, Ankit Tölle, Jonas M. Probability Analysis of PDEs Functional Analysis 35K57, 60H15, 37N25, 47H10, 76S05, 92C15 One standard way to prove existence for deterministic, highly nonlinear PDEs is to use the Schauder-Tychonoff fixed-point theorem. In what follows, we introduce and verify a stochastic variant of the Schauder-Tychonoff theorem. We apply our existence result to nonlinear stochastic diffusion equations with non-Lipschitz perturbations |
| title | A stochastic Schauder-Tychonoff type theorem and its applications |
| topic | Probability Analysis of PDEs Functional Analysis 35K57, 60H15, 37N25, 47H10, 76S05, 92C15 |
| url | https://arxiv.org/abs/2602.17285 |