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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.04684 |
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| _version_ | 1866910194375589888 |
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| author | Ye, Mingkun Zhai, Yafei Zhang, Zuozheng |
| author_facet | Ye, Mingkun Zhai, Yafei Zhang, Zuozheng |
| contents | This paper investigates the ergodicity of stochastic functional differential equations with jumps under the Wasserstein distance by the generalized coupling method. Two key conditions are verified. The first is verified by establishing an exponential decay bound for the coupled segment processes and applying the Girsanov theorem for Itô-Lévy processes. The second is verified through a support theorem developed for an auxiliary process and then extended to the underlying process. Combining these results yields the desired ergodicity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04684 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ergodicity of stochastic functional differential equation with jumps and finite delay Ye, Mingkun Zhai, Yafei Zhang, Zuozheng Probability This paper investigates the ergodicity of stochastic functional differential equations with jumps under the Wasserstein distance by the generalized coupling method. Two key conditions are verified. The first is verified by establishing an exponential decay bound for the coupled segment processes and applying the Girsanov theorem for Itô-Lévy processes. The second is verified through a support theorem developed for an auxiliary process and then extended to the underlying process. Combining these results yields the desired ergodicity. |
| title | Ergodicity of stochastic functional differential equation with jumps and finite delay |
| topic | Probability |
| url | https://arxiv.org/abs/2605.04684 |