Multilevel large deviations and interacting diffusions

Abstract

Let (ξN) be a sequence of random variables with values in a topological space which satisfy the large deviation principle. For each M and each N, let ΞM, N denote the empirical measure associated with M independent copies of ξN. As a main result, we show that (ΞM, N) also satisfies the large deviation principle as M,N→∞. We derive several representations of the associated rate function. These results are then applied to empirical measure processes ΞM, N(t) =M-1 Σi=1N δξiN(t) 0≦t≦T, where (ξ1N,..., ξMN(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]). © 1994 Springer-Verlag.