PROPAGATION OF CHAOS AND THE MCKEAN VLASOV EQUATION IN DUALS OF NUCLEAR SPACES

An interacting system of n stochastic differential equations taking values in the dual of a countable Hilbertian nuclear space is considered. The limit (in probability) of the sequence of empirical measures determined by the above systems as n tends to infinity is identified with the law of the unique solution of the McKean-Vlasov equation. An application of our result to interacting neurons is briefly discussed. The propagation of chaos result obtained in this paper is shown to contain and improve the well-known finite-dimensional results.