Mosco convergence of independent particles and applications to particle systems with self-duality

Abstract: We consider a sequence of Markov processes $\lbrace X_t^n \mid n \in \mathbb{N} \rbrace$ with Dirichlet forms converging in the Mosco sense of Kuwae and Shioya to the Dirichlet form associated with a Markov process $X_t$. Under this assumption, we demonstrate that for any natural number $k$, the sequence of Dirichlet forms corresponding to the Markov processes generated by $k$ independent copies of $\lbrace X_t^n \mid n \in \mathbb{N} \rbrace$ also converges. As expected, the limit of this convergence is the Dirichlet form associated with $k$ independent copies of the process $X_t$. We provide applications of this result in the context of interacting particle systems with Markov moment duality.