Abstract
An interacting system ofn 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 asn 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.
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This research was supported by the Air Force Office of Scientific Research Contract No. F49620-85C-0144. T. S. Chiang would like to thank the Center for Stochastic Processes, University of North Carolina, for hospitality. P. Sundar thanks the Center for Stochastic Processes for his financial support while doing this research.
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Chiang, T.S., Kallianpur, G. & Sundar, P. Propagation of chaos and the McKean-Vlasov equation in duals of nuclear spaces. Appl Math Optim 24, 55–83 (1991). https://doi.org/10.1007/BF01447735
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DOI: https://doi.org/10.1007/BF01447735