Well-Posedness and Ergodicity of Functional Stochastic Partial Differential Equations with Markovian Switching
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916953269993472 |
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| author | Xi, Fubao Ye, Mingkun Zhang, Zuozheng |
| author_facet | Xi, Fubao Ye, Mingkun Zhang, Zuozheng |
| contents | This work focuses on a class of semi-linear functional stochastic partial differential equations with Markovian switching, in which the switching component may have finite or countably infinite states. The well-posedness of the underlying process is obtained by Skorokhod's representation of the switching component. Then, the exponential mixing of such processes in a finite state space is derived by using the so-called remote start method proposed firstly by Prato and Zabczyk in [10]. Finally, the corresponding result in a countable infinite state space is further obtained via the finite partition method. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_13665 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Well-Posedness and Ergodicity of Functional Stochastic Partial Differential Equations with Markovian Switching Xi, Fubao Ye, Mingkun Zhang, Zuozheng Probability 34K34, 34K50, 37A25, 60H15, 60J27 This work focuses on a class of semi-linear functional stochastic partial differential equations with Markovian switching, in which the switching component may have finite or countably infinite states. The well-posedness of the underlying process is obtained by Skorokhod's representation of the switching component. Then, the exponential mixing of such processes in a finite state space is derived by using the so-called remote start method proposed firstly by Prato and Zabczyk in [10]. Finally, the corresponding result in a countable infinite state space is further obtained via the finite partition method. |
| title | Well-Posedness and Ergodicity of Functional Stochastic Partial Differential Equations with Markovian Switching |
| topic | Probability 34K34, 34K50, 37A25, 60H15, 60J27 |
| url | https://arxiv.org/abs/2509.13665 |