Well-Posedness and Ergodicity of Functional Stochastic Partial Differential Equations with Markovian Switching

Fuente: arXiv
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Main Authors: Xi, Fubao, Ye, Mingkun, Zhang, Zuozheng
Format: Preprint
Published: 2025
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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
id 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