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

We consider a sequence of Markov processes Xₜⁿ n ∈ N with Dirichlet forms converging in the Mosco sense of Kuwae and Shioya to the Dirichlet form associated with a Markov process Xₜ. 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 Xₜⁿ n ∈ N also converges. As expected, the limit of this convergence is the Dirichlet form associated with k independent copies of the process Xₜ. We provide applications of this result in the context of interacting particle systems with Markov moment duality.