Asymptotic Behavior of a System of Interacting Nuclear Space-Valued StochasticDifferential Equations Driven by Poisson Random Measures

摘要

In this paper we study a system of interacting stochastic differential equationstaking values in duals of nuclear spaces driven by Poisson random measures. We also consider the McKean-Vlasov equation associated with the system. We show that under suitable conditions the system has a unique solution and the sequence of its empirical distributions converges to the solution of the McKean-Vlasov equation when the size of the system tends to infinity. The results are applied to the voltage potentials of a large system of neurons and the limiting distribution of the empirical measure is obtained. (AN).