Large Deviations for Slow-Fast Mean-Field Diffusions
Wei Hong, Wei Liu, Shiyuan YangAbstract.
The aim of this paper is to investigate the large deviations for a class of slow-fast mean-field diffusions, where the slow process depends on not only the fast process but also their distributions. Due to the perturbations of the fast process and its time marginal law, one cannot prove the large deviations based on verifying the powerful weak convergence criterion directly. To overcome this problem, we employ the functional occupation measure, which, combined with the notion of viable pair and the controls of the feedback form, characterize the limits of controlled sequences and justify the upper and lower bounds of the Laplace principle. As a consequence, the explicit representation formula of the rate function for large deviations is also presented.