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 ∞ 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. © 1991 Springer-Verlag New York Inc.
Publication Source (Journal or Book title)
Applied Mathematics & Optimization
Chiang, T., Kallianpur, G., & Sundar, P. (1991). Propagation of chaos and the McKean-Vlasov equation in duals of nuclear spaces. Applied Mathematics & Optimization, 24 (1), 55-83. https://doi.org/10.1007/BF01447735