Multilevel large deviations and interacting diffusions

Summary Let ( ^N ) be a sequence of random variables with values in a topological space which satisfy the large deviation principle. For eachM and eachN, let ^{M, N} denote the empirical measure associated withM independent copies of ^N . As a main result, we show that ( ^{M, 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 ^{M, N} (t) =M ^–1 _i=1 ^N _i ^N (t) 0tT, where ( ₁ ^N ,..., _M ^N (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]).Research partially supported by a Natural Science and Engineering Research Council of Canada operating grant