Title

Propagation of chaos and the McKean-Vlasov equation in duals of nuclear spaces

Document Type

Article

Publication Date

7-1-1991

Abstract

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

First Page

55

Last Page

83

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