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| Format: | Preprint |
| Veröffentlicht: |
2023
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2305.14479 |
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| _version_ | 1866916161945337856 |
|---|---|
| author | Okazaki, Fumiya |
| author_facet | Okazaki, Fumiya |
| contents | We characterize weakly harmonic maps with respect to non-local Dirichlet forms by Markov processes and martingales. In particular, we can obtain discontinuous martingales on Riemannian manifolds from the image of symmetric stable processes under fractional harmonic maps in a weak sense. Based on this characterization, we also consider the continuity of weakly harmonic maps along the paths of Markov processes and describe the condition for the continuity of harmonic maps by quadratic variations of martingales in some situations containing cases of energy minimizing maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_14479 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Probabilistic characterization of weakly harmonic maps with respect to non-local Dirichlet forms Okazaki, Fumiya Probability 60J46, 58E20 We characterize weakly harmonic maps with respect to non-local Dirichlet forms by Markov processes and martingales. In particular, we can obtain discontinuous martingales on Riemannian manifolds from the image of symmetric stable processes under fractional harmonic maps in a weak sense. Based on this characterization, we also consider the continuity of weakly harmonic maps along the paths of Markov processes and describe the condition for the continuity of harmonic maps by quadratic variations of martingales in some situations containing cases of energy minimizing maps. |
| title | Probabilistic characterization of weakly harmonic maps with respect to non-local Dirichlet forms |
| topic | Probability 60J46, 58E20 |
| url | https://arxiv.org/abs/2305.14479 |