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

Fubao Xi; Mingkun Ye; Zuozheng Zhang

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arXiv · 2509.13665

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

Fubao Xi·Mingkun Ye·Zuozheng Zhang

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Abstract

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.

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Fubao Xi, Mingkun Ye, Zuozheng Zhang. 2025-09-17. Well-Posedness and Ergodicity of Functional Stochastic Partial Differential Equations with Markovian Switching. https://arxiv.org/abs/2509.13665

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