The analysis reveals the well-posedness and ergodicity of inhomogenous birth-death processes, suggesting stability and predictability in dynamic systems.
For a class of time inhomogenous distribution dependent birth-death processes, we derive the well-posedness, Wₚ-estimate, exponential ergodicity, and uniform in time propagation of chaos. These extend the corresponding results derived for distribution dependent SDEs and mean field particle systems. As preparation, a criterion on the well-posedness of inhomogenous jump process is presented in the end of the paper, which should be interesting by itself.
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Wang et al. (2025) studied this question.
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