Summary
Let (ξN) be a sequence of random variables with values in a topological space which satisfy the large deviation principle. For eachM and eachN, let ΞM, N denote the empirical measure associated withM independent copies of ξN. As a main result, we show that (ΞM, N) also satisfies the large deviation principle asM,N→∞. We derive several representations of the associated rate function. These results are then applied to empirical measure processes ΞM, N(t) =M −1 Σ Ni=1 δξ N i (t) 0≦t≦T, where (ξ N1 ,..., ξ N M (t)) is a system of weakly interacting diffusions with noise intensity 1/N. This is a continuation of our previous work on the McKean-Vlasov limit and related hierarchical models ([4], [5]).
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Research partially supported by a Natural Science and Engineering Research Council of Canada operating grant