Switching diffusions with mean-field interactions: limit results, maximum principle, and non-Markov systems

This paper is devoted to switching diffusions with mean-field interactions. We first review some of the recent results. Then we examine a case of systems not driven by Brownian motion but stationary mixing processes. We obtain the limit of the systems by weak convergence analysis together with our limit results on a law of large numbers for switching diffusion processes with mean-field terms.